-
Previous Article
Two-stage model of carcinogenic mutations with the influence of delays
- DCDS-B Home
- This Issue
-
Next Article
Modeling DNA thermal denaturation at the mesoscopic level
Existence of weak solutions for non-local fractional problems via Morse theory
1. | University of Reggio Calabria and CRIOS University Bocconi of Milan, Via dei Bianchi presso Palazzo Zani, 89127 Reggio Calabria, Italy |
2. | Dipartimento P.A.U., Università degli Studi Mediterranea di Reggio Calabria, Salita Melissari - Feo di Vito, 89100 Reggio Calabria |
3. | Department of Mathematics, Heilongjiang Institute of Technology, 150050 Harbin, China |
References:
[1] |
C. O. Alves and S. B. Liu, On superlinear $p(x)$-Laplacian equations in $\mathbbR^N$, Nonlinear Anal., 73 (2010), 2566-2579.
doi: 10.1016/j.na.2010.06.033. |
[2] |
B. Barrios, E. Colorado, A. De Pablo and U. Sanchez, On some critical problems for the fractional Laplacian operator, J. Differential Equations, 252 (2012), 6133-6162.
doi: 10.1016/j.jde.2012.02.023. |
[3] |
T. Bartsch, and S. J. Li, Critical point theory for asymptotically quadratic functionals and applications to problems with resonance, Nonlinear Anal., 28 (1997), 419-441.
doi: 10.1016/0362-546X(95)00167-T. |
[4] |
K. Bogdan, The boundary Harnack principle for the fractional Laplacian, Studia Math., 123 (1997), 43-80. |
[5] |
K. Bogdan and T. Jakubowski, Estimates of heat kernel of fractional Laplacian perturbed by gradient operators, Comm. Math. Phys., 271 (2007), 179-198.
doi: 10.1007/s00220-006-0178-y. |
[6] |
D. Bors, Global solvability of Hammerstein equations with applications to BVP involving fractional Laplacian, Abstr. Appl. Anal., (2013), Art. ID 240863, 10 pp. |
[7] |
D. Bors, Stability of Nonlinear Dirichlet BVPs Governed by Fractional Laplacian, Scientific World Journal, (2014), Art. ID 920537, 10 pp.
doi: 10.1155/2014/920537. |
[8] |
C. Brändle, E. Colorado, A.de Pablo and U. Sánchez, A concave-convex elliptic problem involving the fractional Laplacian, Proc. Roy. Soc. Edinburgh Sect. A, 143 (2013), 39-71.
doi: 10.1017/S0308210511000175. |
[9] |
X. Cabré and J. Tan, Positive solutions of nonlinear problems involving the square root of the Laplacian, Adv. Math., 224 (2010), 2052-2093.
doi: 10.1016/j.aim.2010.01.025. |
[10] |
L. Caffarelli, J. M. Roquejoffre and Y. Sire, Variational problems for free boundaries for the fractional Laplacian, J. Eur. Math. Soc., 12 (2010), 1151-1179.}
doi: 10.4171/JEMS/226. |
[11] |
L. Caffarelli, S. Salsa and L. Silvestre, Regularity estimates for the solution and the free boundary of the obstacle problem for the fractional Laplacian, Invent. Math., 171 (2008), 425-461.
doi: 10.1007/s00222-007-0086-6. |
[12] |
L. Caffarelli and L. Silvestre, An extension problem related to the fractional Laplacian, Comm. Partial Differential Equations, 32 (2007), 1245-1260.
doi: 10.1080/03605300600987306. |
[13] |
A. Capella, Solutions of a pure critical exponent problem involving the half-Laplacian in annular-shaped domains, Commun. Pure Appl. Anal., 10 (2011), 1645-1662.
doi: 10.3934/cpaa.2011.10.1645. |
[14] |
K. C. Chang, Infinite Dimensional Morse Theory and Multiple Solution Problems, Birkhäuser, Boston, 1993.
doi: 10.1007/978-1-4612-0385-8. |
[15] |
S. Y. A. Chang and M. del Mar González, Fractional Laplacian in conformal geometry, Adv. Math., 226 (2011), 1410-1432.
doi: 10.1016/j.aim.2010.07.016. |
[16] |
M. del Mar González, Gamma convergence of an energy functional related to the fractional Laplacian, Calc. Var. Partial Differential Equations, 36 (2009), 173-210.
doi: 10.1007/s00526-009-0225-6. |
[17] |
F. Fang, and S. B. Liu, Nontrivial solutions of superlinear $p$-Laplacian equations, J. Math. Anal. Appl., 351 (2009), 138-146.
doi: 10.1016/j.jmaa.2008.09.064. |
[18] |
A. Fiscella, R. Servadei and E. Valdinoci, A resonance problem for non-local elliptic operators, Z. Anal. Anwendungen, 32 (2013), 411-431.
doi: 10.4171/ZAA/1492. |
[19] |
D. Idczak and R. Kamocki, On the existence and uniqueness and formula for the solution of R-L fractional Cauchy problem in $\mathbbR^n$, Fractional Calculus & Applied Analysis, 14 (2011), 538-553.
doi: 10.2478/s13540-011-0033-5. |
[20] |
D. Idczak and R. Kamocki, Fractional differential repetitive process with Riemann-Liouville and Caputo derivatives, Multidim. Syst. Sign Process, (2013).
doi: 10.1007/s11045-013-0249-0. |
[21] |
D. Idczak, R. Kamocki and M. Majewski, Fractional continuous Roesser model with Reimann-Liouville derivative, 8th Int. workshop on multidimensional Systems, (2013), 33-38. |
[22] |
D. Idczak, R. Kamocki and M. Majewski, On a fractional continuous counterpart of Fornasini-Marchesini model, 8th Int. Workshop on Multidimensional Systems, (2013), 45-49. |
[23] |
D. Idczak and M. Majewski, Fractional fundamental lemma of order $\alpha\in (n-\frac{1}{2}, n)$ with $n\in\mathbbN, n\geq2$, Dynamic System and Applications, 12 (2012), 251-268. |
[24] |
D. Idczak and M. Majewski, Compactness of fractional embeddings for boundary value problems, IEEE, 7 (2013), 599-603. |
[25] |
D. Idczak, A. Skowron and S. Walczak, Sensitivity of a fractional integrodifferential Cauchy problem of Volterra type, Abstract and Applied Analysis, 2013 (2013), 1-8. |
[26] |
D. Idczak, and S. Walczak, A fractional imbedding theorem, Fractional Calculus & Applied Analysis, 15 (2012), 418-425.
doi: 10.2478/s13540-012-0030-3. |
[27] |
D. Idczak and S. Walczak, Compactness of fractional imbeddings, IEEE, 2 (2012), 585-588.
doi: 10.1109/MMAR.2012.6347820. |
[28] |
D. Idczak and S. Walczak, Fractional Sobolev spaces via Riemann-Liouville derivatives, Journal of Function Spaces and Applications, 2013 (2013), 1-15. |
[29] |
L. Jeanjean, On the existence of bounded Palais-Smale sequences and application to a Landesman-Lazer type problem set on $\mathbbR^N$, Proc. Roy. Soc. Edinburgh, 129 (1999), 787-809.
doi: 10.1017/S0308210500013147. |
[30] |
K. Kaleta and T. Kulczycki, Intrinsic ultracontractivity for Schrödinger operators based on fractional Laplacians, Potential Anal., 33 (2010), 313-339.
doi: 10.1007/s11118-010-9170-4. |
[31] |
R. Kamocki and M. Majewski, On a fractional Dirichlet problem, IEEE, 2 (2012), 60-63.
doi: 10.1109/MMAR.2012.6347911. |
[32] |
A. Kristály, V. Rădulescu and Cs. Varga, Variational Principles in Mathematical Physics, Geometry, and Economics: Qualitative Analysis of Nonlinear Equations and Unilateral Problems, Encyclopedia of Mathematics and its Applications, No. 136, Cambridge University Press, Cambridge, 2010.
doi: 10.1017/CBO9780511760631. |
[33] |
S. B. Liu, On ground states of superlinear $p$-Laplacian equations in $\mathbbR^N$, J. Math. Anal. Appl., 361 (2010), 48-58.
doi: 10.1016/j.jmaa.2009.09.016. |
[34] |
S. B. Liu, On superlinear problems without Ambrosetti-Rabinowitz condition, Nonlinear Anal., 73 (2010), 788-795.
doi: 10.1016/j.na.2010.04.016. |
[35] |
S. B. Liu, Existence of solutions to a superlinear $p$-Laplacian equation, Electron J. Differential Equations, 66 (2001), 1-6. |
[36] |
J. Q. Liu and J. B. Su, Remarks on multiple nontrivial solutions for quasi-linear resonant problems, J. Math. Anal. Appl., 258 (2001), 209-222.
doi: 10.1006/jmaa.2000.7374. |
[37] |
Q. S. Liu and J. B. Su, Existence and multiplicity results for Dirichlet problems with $p$-Laplacian, J. Math. Anal. Appl., 281 (2003), 587-601. |
[38] |
G. Molica Bisci, Fractional equations with bounded primitive, Appl. Math. Lett., 27 (2014), 53-58.
doi: 10.1016/j.aml.2013.07.011. |
[39] |
G. Molica Bisci, Sequences of weak solutions for fractional equations, Math. Res. Lett., 21 (2014), 1-13. |
[40] |
G. Molica Bisci and B. A. Pansera, Three weak solutions for nonlocal fractional equations, Adv. Nonlinear Stud., 14 (2014), 591-601. |
[41] |
G. Molica Bisci and D. Repovs, Higher nonlocal problems with bounded potential, J. Math. Anal. Appl., 420 (2014), 167-176. |
[42] |
G. Molica Bisci and R. Servadei, A bifurcation result for non-local fractional equations,, to appear in Analysis and Applications., ().
doi: 10.1142/S0219530514500067. |
[43] |
K. Perera, R. P. Agarwal and D. O'Regan, Morse Theoretic Aspects of $p$-Laplacian Type Operatiors, Mathematical Surveys and Monographs, 161, American Mathematical Society, Providence, RI, 2010.
doi: 10.1090/surv/161. |
[44] |
X. Ros-Oton and J. Serra, Fractional Laplacian: Pohozaev identity and nonexistence results, C. R. Math. Acad. Sci. Paris, 350 (2012), 505-508.
doi: 10.1016/j.crma.2012.05.011. |
[45] |
X. Ros-Oton and J. Serra, The Dirichlet problem for the fractional Laplacian: Regularity up to the boundary, J. Math. Pures Appl., 101 (2014), 275-302.
doi: 10.1016/j.matpur.2013.06.003. |
[46] |
S. Serfaty and J. Luis Vazquez, A mean field equation as limit of nonlinear diffusions with fractional Laplacian operators, Calc. Var. Partial Differential Equations, 49 (2014), 1091-1120.
doi: 10.1007/s00526-013-0613-9. |
[47] |
R. Servadei, Infinitely many solutions for fractional Laplace equations with subcritical nonlinearity, Contemp. Math., 595 (2013), 317-340.
doi: 10.1090/conm/595/11809. |
[48] |
R. Servadei and E. Valdinoci, Lewy-Stampacchia type estimates for variational inequalities driven by (non)local operators, Rev. Mat. Iberoam., 29 (2013), 1091-1126.
doi: 10.4171/RMI/750. |
[49] |
R. Servadei and E. Valdinoci, Mountain Pass solutions for non-local elliptic operators, J. Math. Anal. Appl., 389 (2012), 887-898.
doi: 10.1016/j.jmaa.2011.12.032. |
show all references
References:
[1] |
C. O. Alves and S. B. Liu, On superlinear $p(x)$-Laplacian equations in $\mathbbR^N$, Nonlinear Anal., 73 (2010), 2566-2579.
doi: 10.1016/j.na.2010.06.033. |
[2] |
B. Barrios, E. Colorado, A. De Pablo and U. Sanchez, On some critical problems for the fractional Laplacian operator, J. Differential Equations, 252 (2012), 6133-6162.
doi: 10.1016/j.jde.2012.02.023. |
[3] |
T. Bartsch, and S. J. Li, Critical point theory for asymptotically quadratic functionals and applications to problems with resonance, Nonlinear Anal., 28 (1997), 419-441.
doi: 10.1016/0362-546X(95)00167-T. |
[4] |
K. Bogdan, The boundary Harnack principle for the fractional Laplacian, Studia Math., 123 (1997), 43-80. |
[5] |
K. Bogdan and T. Jakubowski, Estimates of heat kernel of fractional Laplacian perturbed by gradient operators, Comm. Math. Phys., 271 (2007), 179-198.
doi: 10.1007/s00220-006-0178-y. |
[6] |
D. Bors, Global solvability of Hammerstein equations with applications to BVP involving fractional Laplacian, Abstr. Appl. Anal., (2013), Art. ID 240863, 10 pp. |
[7] |
D. Bors, Stability of Nonlinear Dirichlet BVPs Governed by Fractional Laplacian, Scientific World Journal, (2014), Art. ID 920537, 10 pp.
doi: 10.1155/2014/920537. |
[8] |
C. Brändle, E. Colorado, A.de Pablo and U. Sánchez, A concave-convex elliptic problem involving the fractional Laplacian, Proc. Roy. Soc. Edinburgh Sect. A, 143 (2013), 39-71.
doi: 10.1017/S0308210511000175. |
[9] |
X. Cabré and J. Tan, Positive solutions of nonlinear problems involving the square root of the Laplacian, Adv. Math., 224 (2010), 2052-2093.
doi: 10.1016/j.aim.2010.01.025. |
[10] |
L. Caffarelli, J. M. Roquejoffre and Y. Sire, Variational problems for free boundaries for the fractional Laplacian, J. Eur. Math. Soc., 12 (2010), 1151-1179.}
doi: 10.4171/JEMS/226. |
[11] |
L. Caffarelli, S. Salsa and L. Silvestre, Regularity estimates for the solution and the free boundary of the obstacle problem for the fractional Laplacian, Invent. Math., 171 (2008), 425-461.
doi: 10.1007/s00222-007-0086-6. |
[12] |
L. Caffarelli and L. Silvestre, An extension problem related to the fractional Laplacian, Comm. Partial Differential Equations, 32 (2007), 1245-1260.
doi: 10.1080/03605300600987306. |
[13] |
A. Capella, Solutions of a pure critical exponent problem involving the half-Laplacian in annular-shaped domains, Commun. Pure Appl. Anal., 10 (2011), 1645-1662.
doi: 10.3934/cpaa.2011.10.1645. |
[14] |
K. C. Chang, Infinite Dimensional Morse Theory and Multiple Solution Problems, Birkhäuser, Boston, 1993.
doi: 10.1007/978-1-4612-0385-8. |
[15] |
S. Y. A. Chang and M. del Mar González, Fractional Laplacian in conformal geometry, Adv. Math., 226 (2011), 1410-1432.
doi: 10.1016/j.aim.2010.07.016. |
[16] |
M. del Mar González, Gamma convergence of an energy functional related to the fractional Laplacian, Calc. Var. Partial Differential Equations, 36 (2009), 173-210.
doi: 10.1007/s00526-009-0225-6. |
[17] |
F. Fang, and S. B. Liu, Nontrivial solutions of superlinear $p$-Laplacian equations, J. Math. Anal. Appl., 351 (2009), 138-146.
doi: 10.1016/j.jmaa.2008.09.064. |
[18] |
A. Fiscella, R. Servadei and E. Valdinoci, A resonance problem for non-local elliptic operators, Z. Anal. Anwendungen, 32 (2013), 411-431.
doi: 10.4171/ZAA/1492. |
[19] |
D. Idczak and R. Kamocki, On the existence and uniqueness and formula for the solution of R-L fractional Cauchy problem in $\mathbbR^n$, Fractional Calculus & Applied Analysis, 14 (2011), 538-553.
doi: 10.2478/s13540-011-0033-5. |
[20] |
D. Idczak and R. Kamocki, Fractional differential repetitive process with Riemann-Liouville and Caputo derivatives, Multidim. Syst. Sign Process, (2013).
doi: 10.1007/s11045-013-0249-0. |
[21] |
D. Idczak, R. Kamocki and M. Majewski, Fractional continuous Roesser model with Reimann-Liouville derivative, 8th Int. workshop on multidimensional Systems, (2013), 33-38. |
[22] |
D. Idczak, R. Kamocki and M. Majewski, On a fractional continuous counterpart of Fornasini-Marchesini model, 8th Int. Workshop on Multidimensional Systems, (2013), 45-49. |
[23] |
D. Idczak and M. Majewski, Fractional fundamental lemma of order $\alpha\in (n-\frac{1}{2}, n)$ with $n\in\mathbbN, n\geq2$, Dynamic System and Applications, 12 (2012), 251-268. |
[24] |
D. Idczak and M. Majewski, Compactness of fractional embeddings for boundary value problems, IEEE, 7 (2013), 599-603. |
[25] |
D. Idczak, A. Skowron and S. Walczak, Sensitivity of a fractional integrodifferential Cauchy problem of Volterra type, Abstract and Applied Analysis, 2013 (2013), 1-8. |
[26] |
D. Idczak, and S. Walczak, A fractional imbedding theorem, Fractional Calculus & Applied Analysis, 15 (2012), 418-425.
doi: 10.2478/s13540-012-0030-3. |
[27] |
D. Idczak and S. Walczak, Compactness of fractional imbeddings, IEEE, 2 (2012), 585-588.
doi: 10.1109/MMAR.2012.6347820. |
[28] |
D. Idczak and S. Walczak, Fractional Sobolev spaces via Riemann-Liouville derivatives, Journal of Function Spaces and Applications, 2013 (2013), 1-15. |
[29] |
L. Jeanjean, On the existence of bounded Palais-Smale sequences and application to a Landesman-Lazer type problem set on $\mathbbR^N$, Proc. Roy. Soc. Edinburgh, 129 (1999), 787-809.
doi: 10.1017/S0308210500013147. |
[30] |
K. Kaleta and T. Kulczycki, Intrinsic ultracontractivity for Schrödinger operators based on fractional Laplacians, Potential Anal., 33 (2010), 313-339.
doi: 10.1007/s11118-010-9170-4. |
[31] |
R. Kamocki and M. Majewski, On a fractional Dirichlet problem, IEEE, 2 (2012), 60-63.
doi: 10.1109/MMAR.2012.6347911. |
[32] |
A. Kristály, V. Rădulescu and Cs. Varga, Variational Principles in Mathematical Physics, Geometry, and Economics: Qualitative Analysis of Nonlinear Equations and Unilateral Problems, Encyclopedia of Mathematics and its Applications, No. 136, Cambridge University Press, Cambridge, 2010.
doi: 10.1017/CBO9780511760631. |
[33] |
S. B. Liu, On ground states of superlinear $p$-Laplacian equations in $\mathbbR^N$, J. Math. Anal. Appl., 361 (2010), 48-58.
doi: 10.1016/j.jmaa.2009.09.016. |
[34] |
S. B. Liu, On superlinear problems without Ambrosetti-Rabinowitz condition, Nonlinear Anal., 73 (2010), 788-795.
doi: 10.1016/j.na.2010.04.016. |
[35] |
S. B. Liu, Existence of solutions to a superlinear $p$-Laplacian equation, Electron J. Differential Equations, 66 (2001), 1-6. |
[36] |
J. Q. Liu and J. B. Su, Remarks on multiple nontrivial solutions for quasi-linear resonant problems, J. Math. Anal. Appl., 258 (2001), 209-222.
doi: 10.1006/jmaa.2000.7374. |
[37] |
Q. S. Liu and J. B. Su, Existence and multiplicity results for Dirichlet problems with $p$-Laplacian, J. Math. Anal. Appl., 281 (2003), 587-601. |
[38] |
G. Molica Bisci, Fractional equations with bounded primitive, Appl. Math. Lett., 27 (2014), 53-58.
doi: 10.1016/j.aml.2013.07.011. |
[39] |
G. Molica Bisci, Sequences of weak solutions for fractional equations, Math. Res. Lett., 21 (2014), 1-13. |
[40] |
G. Molica Bisci and B. A. Pansera, Three weak solutions for nonlocal fractional equations, Adv. Nonlinear Stud., 14 (2014), 591-601. |
[41] |
G. Molica Bisci and D. Repovs, Higher nonlocal problems with bounded potential, J. Math. Anal. Appl., 420 (2014), 167-176. |
[42] |
G. Molica Bisci and R. Servadei, A bifurcation result for non-local fractional equations,, to appear in Analysis and Applications., ().
doi: 10.1142/S0219530514500067. |
[43] |
K. Perera, R. P. Agarwal and D. O'Regan, Morse Theoretic Aspects of $p$-Laplacian Type Operatiors, Mathematical Surveys and Monographs, 161, American Mathematical Society, Providence, RI, 2010.
doi: 10.1090/surv/161. |
[44] |
X. Ros-Oton and J. Serra, Fractional Laplacian: Pohozaev identity and nonexistence results, C. R. Math. Acad. Sci. Paris, 350 (2012), 505-508.
doi: 10.1016/j.crma.2012.05.011. |
[45] |
X. Ros-Oton and J. Serra, The Dirichlet problem for the fractional Laplacian: Regularity up to the boundary, J. Math. Pures Appl., 101 (2014), 275-302.
doi: 10.1016/j.matpur.2013.06.003. |
[46] |
S. Serfaty and J. Luis Vazquez, A mean field equation as limit of nonlinear diffusions with fractional Laplacian operators, Calc. Var. Partial Differential Equations, 49 (2014), 1091-1120.
doi: 10.1007/s00526-013-0613-9. |
[47] |
R. Servadei, Infinitely many solutions for fractional Laplace equations with subcritical nonlinearity, Contemp. Math., 595 (2013), 317-340.
doi: 10.1090/conm/595/11809. |
[48] |
R. Servadei and E. Valdinoci, Lewy-Stampacchia type estimates for variational inequalities driven by (non)local operators, Rev. Mat. Iberoam., 29 (2013), 1091-1126.
doi: 10.4171/RMI/750. |
[49] |
R. Servadei and E. Valdinoci, Mountain Pass solutions for non-local elliptic operators, J. Math. Anal. Appl., 389 (2012), 887-898.
doi: 10.1016/j.jmaa.2011.12.032. |
[1] |
Ramasamy Subashini, Chokkalingam Ravichandran, Kasthurisamy Jothimani, Haci Mehmet Baskonus. Existence results of Hilfer integro-differential equations with fractional order. Discrete and Continuous Dynamical Systems - S, 2020, 13 (3) : 911-923. doi: 10.3934/dcdss.2020053 |
[2] |
Sertan Alkan. A new solution method for nonlinear fractional integro-differential equations. Discrete and Continuous Dynamical Systems - S, 2015, 8 (6) : 1065-1077. doi: 10.3934/dcdss.2015.8.1065 |
[3] |
Ji Shu, Linyan Li, Xin Huang, Jian Zhang. Limiting behavior of fractional stochastic integro-Differential equations on unbounded domains. Mathematical Control and Related Fields, 2021, 11 (4) : 715-737. doi: 10.3934/mcrf.2020044 |
[4] |
Michel Chipot, Senoussi Guesmia. On a class of integro-differential problems. Communications on Pure and Applied Analysis, 2010, 9 (5) : 1249-1262. doi: 10.3934/cpaa.2010.9.1249 |
[5] |
Miloud Moussai. Application of the bernstein polynomials for solving the nonlinear fractional type Volterra integro-differential equation with caputo fractional derivatives. Numerical Algebra, Control and Optimization, 2021 doi: 10.3934/naco.2021021 |
[6] |
Eduardo Cuesta. Asymptotic behaviour of the solutions of fractional integro-differential equations and some time discretizations. Conference Publications, 2007, 2007 (Special) : 277-285. doi: 10.3934/proc.2007.2007.277 |
[7] |
Yin Yang, Sujuan Kang, Vasiliy I. Vasil'ev. The Jacobi spectral collocation method for fractional integro-differential equations with non-smooth solutions. Electronic Research Archive, 2020, 28 (3) : 1161-1189. doi: 10.3934/era.2020064 |
[8] |
Seda İğret Araz. New class of volterra integro-differential equations with fractal-fractional operators: Existence, uniqueness and numerical scheme. Discrete and Continuous Dynamical Systems - S, 2021, 14 (7) : 2297-2309. doi: 10.3934/dcdss.2021053 |
[9] |
Xinjie Dai, Aiguo Xiao, Weiping Bu. Stochastic fractional integro-differential equations with weakly singular kernels: Well-posedness and Euler–Maruyama approximation. Discrete and Continuous Dynamical Systems - B, 2021 doi: 10.3934/dcdsb.2021225 |
[10] |
Huy Tuan Nguyen, Huu Can Nguyen, Renhai Wang, Yong Zhou. Initial value problem for fractional Volterra integro-differential equations with Caputo derivative. Discrete and Continuous Dynamical Systems - B, 2021, 26 (12) : 6483-6510. doi: 10.3934/dcdsb.2021030 |
[11] |
Priscila Santos Ramos, J. Vanterler da C. Sousa, E. Capelas de Oliveira. Existence and uniqueness of mild solutions for quasi-linear fractional integro-differential equations. Evolution Equations and Control Theory, 2022, 11 (1) : 1-24. doi: 10.3934/eect.2020100 |
[12] |
Ankit Kumar, Kamal Jeet, Ramesh Kumar Vats. Controllability of Hilfer fractional integro-differential equations of Sobolev-type with a nonlocal condition in a Banach space. Evolution Equations and Control Theory, 2022, 11 (2) : 605-619. doi: 10.3934/eect.2021016 |
[13] |
Olivier Bonnefon, Jérôme Coville, Jimmy Garnier, Lionel Roques. Inside dynamics of solutions of integro-differential equations. Discrete and Continuous Dynamical Systems - B, 2014, 19 (10) : 3057-3085. doi: 10.3934/dcdsb.2014.19.3057 |
[14] |
Nestor Guillen, Russell W. Schwab. Neumann homogenization via integro-differential operators. Discrete and Continuous Dynamical Systems, 2016, 36 (7) : 3677-3703. doi: 10.3934/dcds.2016.36.3677 |
[15] |
Paola Loreti, Daniela Sforza. Observability of $N$-dimensional integro-differential systems. Discrete and Continuous Dynamical Systems - S, 2016, 9 (3) : 745-757. doi: 10.3934/dcdss.2016026 |
[16] |
Mohammed Al Horani, Angelo Favini, Hiroki Tanabe. Singular integro-differential equations with applications. Evolution Equations and Control Theory, 2021 doi: 10.3934/eect.2021051 |
[17] |
Mohammed Al Horani, Angelo Favini, Hiroki Tanabe. Inverse problems on degenerate integro-differential equations. Discrete and Continuous Dynamical Systems - S, 2022 doi: 10.3934/dcdss.2022025 |
[18] |
Ichrak Bouacida, Mourad Kerboua, Sami Segni. Controllability results for Sobolev type $ \psi - $Hilfer fractional backward perturbed integro-differential equations in Hilbert space. Evolution Equations and Control Theory, 2022 doi: 10.3934/eect.2022028 |
[19] |
Jean-Michel Roquejoffre, Juan-Luis Vázquez. Ignition and propagation in an integro-differential model for spherical flames. Discrete and Continuous Dynamical Systems - B, 2002, 2 (3) : 379-387. doi: 10.3934/dcdsb.2002.2.379 |
[20] |
Tomás Caraballo, P.E. Kloeden. Non-autonomous attractors for integro-differential evolution equations. Discrete and Continuous Dynamical Systems - S, 2009, 2 (1) : 17-36. doi: 10.3934/dcdss.2009.2.17 |
2020 Impact Factor: 1.327
Tools
Metrics
Other articles
by authors
[Back to Top]