-
Previous Article
Periodic solutions of the Brillouin electron beam focusing equation
- CPAA Home
- This Issue
-
Next Article
Quasilinear retarded differential equations with functional dependence on piecewise constant argument
Existence and uniqueness of singular solutions for elliptic equation on the hyperbolic space
1. | Department of Mathematics, National Central University, Chung-Li, 32001, Taiwan |
2. | Department of Mathematics, National Central University, Chung-Li 32001 |
3. | Department of Mathematical Sciences, Osaka Prefecture University, 1-1 Gakuen-cho, Naka-ku, Sakai, 599-8531 |
References:
[1] |
S. Bae, Separation structure of positive radial solutions of a semilinear elliptic equation in $R^n$,, J. Differential Equations, 194 (2003), 460.
doi: 10.1006/jdeq.2001.4162. |
[2] |
S. Bae and T. K. Chang, On a class of semilinear elliptic equations in $R^n$,, J. Differential Equations, 185 (2002), 225.
doi: 10.1016/s0022-396(03)00172-4. |
[3] |
C. Bandle, A. Brillard and M. Flucher, Green's function, harmonic transplantation and best Sobolev constant in spaces of constant curvature,, Trans. Amer. Math. Soc., 350 (1998), 1103.
doi: 10.1090/S0002-9947-98-02085-6. |
[4] |
C. Bandle and Y. Kabeya, On the positive, "radial" solutions of a semilinear elliptic equation on $H^N$,, Adv. Nonlinear Anal., 1 (2012), 1.
doi: 10.1515/ana-2011-0004. |
[5] |
C. Bandle and M. Marcus, The positive radial solutions of a class of semilinear elliptic equations,, J. Reine Angew. Math., 401 (1989), 25.
|
[6] |
M. Bonforte, F. Gazzola, G. Grillo and J. L. Vazquez, Classification of radial solutions to the Emden-Fowler equation on the hyperbolic space,, Cal. Var. Partial Differential Equations, 46 (2013), 375.
|
[7] |
J.-L. Chern, Z.-Y. Chen, J-H. Chen and Y.-L. Tang, On the classification of standing wave solutions for the Schrödinger equation,, Comm. Partial Differential Equations, 35 (2010), 275.
doi: 10.1080/03605300903419767. |
[8] |
B. Gidas, W.-M. Ni and L. Nirenberg, Symmetry and related properties via the maximum principle,, Comm. Math. Phys., 68 (1979), 209.
doi: 10.1007/BF01221125. |
[9] |
B. Gidas, W.-M. Ni and L. Nirenberg, Symmetry of positive solutions of nonlinear elliptic equations in $R^n$,, Adv. Math. Suppl. Stud., 7A (1981), 369.
|
[10] |
A. Grigor'yan, "Heat Kernel and Analysis on Manifolds'',, AMS, (2009).
|
[11] |
C. Gui, W.-M. Ni and X.-F. Wang, On the stability and instability of positive steady states of a semilinear heat equation in $R^n$,, Comm. Pure Appl. Math., 45 (1992), 1153.
doi: 10.1002/cpa.3160450906. |
[12] |
P. Hartman, "Ordinary Differential Equations'',, Birkh\, (1982).
|
[13] |
D. D. Joseph and T. S. Lundgren, Quasilinear Dirichlet problems driven by positive sources,, Arch. Rational Mech. Anal., 49 (1973), 241.
|
[14] |
S. Kumaresan and J. Prajapat, Analogue of Gidas-Ni-Nirenberg result in hyperbolic space and sphere,, Rend. Inst. Math. Univ. Trieste, 30 (1998), 107.
|
[15] |
Y. Li, Asymptotic behavior of positive solutions of equation $\Delta u + K(x)u^p = 0$ in $R^n$,, J. Differential Equations, 95 (1992), 304.
doi: 10.1016/0022-0396(92)90034-K. |
[16] |
Y. Liu, Y. Li and Y. Deng, Separation property of solutions for a semilinear elliptic equation,, J. Differential Equations, 163 (2000), 381.
doi: 10.1006/jdeq.1999.3735. |
[17] |
G. Mancini and K. Sandeep, On a semilinear elliptic equation in $H^n$,, Ann. Scuola Norm. Sup. Pisa Cl. Sci., 7 (2008), 635.
|
[18] |
W.-M. Ni, On the positive radial solutions of some semilinear elliptic equations on $R^n$,, Appl. Math. Optim., 9 (1983), 373.
|
[19] |
W.-M. Ni and S. Yotsutani, Semilinear elliptic equations of Matukuma-type and related topics,, Japan J. Appl. Math., 5 (1988), 1.
|
[20] |
S. Stapelkamp, The Brezis-Nirenberg problem on $H^n$: existence and uniqueness of solutions, in "Elliptic and Parabolic Problems- Rolduc and Gaeta 2001,'', Bemelmans et al. ed., (2002), 283. Google Scholar |
[21] |
X.-F. Wang, On Cauchy Problem for reaction-diffusion equations,, Trans. Amer. Math. Soc., 337 (1993), 549.
doi: 10.1090/S0002-9947-1993-1153015-5. |
show all references
References:
[1] |
S. Bae, Separation structure of positive radial solutions of a semilinear elliptic equation in $R^n$,, J. Differential Equations, 194 (2003), 460.
doi: 10.1006/jdeq.2001.4162. |
[2] |
S. Bae and T. K. Chang, On a class of semilinear elliptic equations in $R^n$,, J. Differential Equations, 185 (2002), 225.
doi: 10.1016/s0022-396(03)00172-4. |
[3] |
C. Bandle, A. Brillard and M. Flucher, Green's function, harmonic transplantation and best Sobolev constant in spaces of constant curvature,, Trans. Amer. Math. Soc., 350 (1998), 1103.
doi: 10.1090/S0002-9947-98-02085-6. |
[4] |
C. Bandle and Y. Kabeya, On the positive, "radial" solutions of a semilinear elliptic equation on $H^N$,, Adv. Nonlinear Anal., 1 (2012), 1.
doi: 10.1515/ana-2011-0004. |
[5] |
C. Bandle and M. Marcus, The positive radial solutions of a class of semilinear elliptic equations,, J. Reine Angew. Math., 401 (1989), 25.
|
[6] |
M. Bonforte, F. Gazzola, G. Grillo and J. L. Vazquez, Classification of radial solutions to the Emden-Fowler equation on the hyperbolic space,, Cal. Var. Partial Differential Equations, 46 (2013), 375.
|
[7] |
J.-L. Chern, Z.-Y. Chen, J-H. Chen and Y.-L. Tang, On the classification of standing wave solutions for the Schrödinger equation,, Comm. Partial Differential Equations, 35 (2010), 275.
doi: 10.1080/03605300903419767. |
[8] |
B. Gidas, W.-M. Ni and L. Nirenberg, Symmetry and related properties via the maximum principle,, Comm. Math. Phys., 68 (1979), 209.
doi: 10.1007/BF01221125. |
[9] |
B. Gidas, W.-M. Ni and L. Nirenberg, Symmetry of positive solutions of nonlinear elliptic equations in $R^n$,, Adv. Math. Suppl. Stud., 7A (1981), 369.
|
[10] |
A. Grigor'yan, "Heat Kernel and Analysis on Manifolds'',, AMS, (2009).
|
[11] |
C. Gui, W.-M. Ni and X.-F. Wang, On the stability and instability of positive steady states of a semilinear heat equation in $R^n$,, Comm. Pure Appl. Math., 45 (1992), 1153.
doi: 10.1002/cpa.3160450906. |
[12] |
P. Hartman, "Ordinary Differential Equations'',, Birkh\, (1982).
|
[13] |
D. D. Joseph and T. S. Lundgren, Quasilinear Dirichlet problems driven by positive sources,, Arch. Rational Mech. Anal., 49 (1973), 241.
|
[14] |
S. Kumaresan and J. Prajapat, Analogue of Gidas-Ni-Nirenberg result in hyperbolic space and sphere,, Rend. Inst. Math. Univ. Trieste, 30 (1998), 107.
|
[15] |
Y. Li, Asymptotic behavior of positive solutions of equation $\Delta u + K(x)u^p = 0$ in $R^n$,, J. Differential Equations, 95 (1992), 304.
doi: 10.1016/0022-0396(92)90034-K. |
[16] |
Y. Liu, Y. Li and Y. Deng, Separation property of solutions for a semilinear elliptic equation,, J. Differential Equations, 163 (2000), 381.
doi: 10.1006/jdeq.1999.3735. |
[17] |
G. Mancini and K. Sandeep, On a semilinear elliptic equation in $H^n$,, Ann. Scuola Norm. Sup. Pisa Cl. Sci., 7 (2008), 635.
|
[18] |
W.-M. Ni, On the positive radial solutions of some semilinear elliptic equations on $R^n$,, Appl. Math. Optim., 9 (1983), 373.
|
[19] |
W.-M. Ni and S. Yotsutani, Semilinear elliptic equations of Matukuma-type and related topics,, Japan J. Appl. Math., 5 (1988), 1.
|
[20] |
S. Stapelkamp, The Brezis-Nirenberg problem on $H^n$: existence and uniqueness of solutions, in "Elliptic and Parabolic Problems- Rolduc and Gaeta 2001,'', Bemelmans et al. ed., (2002), 283. Google Scholar |
[21] |
X.-F. Wang, On Cauchy Problem for reaction-diffusion equations,, Trans. Amer. Math. Soc., 337 (1993), 549.
doi: 10.1090/S0002-9947-1993-1153015-5. |
[1] |
Xiaoming Wang. Quasi-periodic solutions for a class of second order differential equations with a nonlinear damping term. Discrete & Continuous Dynamical Systems - S, 2017, 10 (3) : 543-556. doi: 10.3934/dcdss.2017027 |
[2] |
Elvise Berchio, Filippo Gazzola, Dario Pierotti. Nodal solutions to critical growth elliptic problems under Steklov boundary conditions. Communications on Pure & Applied Analysis, 2009, 8 (2) : 533-557. doi: 10.3934/cpaa.2009.8.533 |
[3] |
Kin Ming Hui, Soojung Kim. Asymptotic large time behavior of singular solutions of the fast diffusion equation. Discrete & Continuous Dynamical Systems - A, 2017, 37 (11) : 5943-5977. doi: 10.3934/dcds.2017258 |
[4] |
Yanqin Fang, Jihui Zhang. Multiplicity of solutions for the nonlinear Schrödinger-Maxwell system. Communications on Pure & Applied Analysis, 2011, 10 (4) : 1267-1279. doi: 10.3934/cpaa.2011.10.1267 |
[5] |
A. Aghajani, S. F. Mottaghi. Regularity of extremal solutions of semilinaer fourth-order elliptic problems with general nonlinearities. Communications on Pure & Applied Analysis, 2018, 17 (3) : 887-898. doi: 10.3934/cpaa.2018044 |
[6] |
Irena PawŃow, Wojciech M. Zajączkowski. Global regular solutions to three-dimensional thermo-visco-elasticity with nonlinear temperature-dependent specific heat. Communications on Pure & Applied Analysis, 2017, 16 (4) : 1331-1372. doi: 10.3934/cpaa.2017065 |
[7] |
Jaume Llibre, Luci Any Roberto. On the periodic solutions of a class of Duffing differential equations. Discrete & Continuous Dynamical Systems - A, 2013, 33 (1) : 277-282. doi: 10.3934/dcds.2013.33.277 |
[8] |
Yimin Zhang, Youjun Wang, Yaotian Shen. Solutions for quasilinear Schrödinger equations with critical Sobolev-Hardy exponents. Communications on Pure & Applied Analysis, 2011, 10 (4) : 1037-1054. doi: 10.3934/cpaa.2011.10.1037 |
[9] |
Vladimir Georgiev, Sandra Lucente. Focusing nlkg equation with singular potential. Communications on Pure & Applied Analysis, 2018, 17 (4) : 1387-1406. doi: 10.3934/cpaa.2018068 |
[10] |
Lucas C. F. Ferreira, Jhean E. Pérez-López, Élder J. Villamizar-Roa. On the product in Besov-Lorentz-Morrey spaces and existence of solutions for the stationary Boussinesq equations. Communications on Pure & Applied Analysis, 2018, 17 (6) : 2423-2439. doi: 10.3934/cpaa.2018115 |
[11] |
Elena Bonetti, Pierluigi Colli, Gianni Gilardi. Singular limit of an integrodifferential system related to the entropy balance. Discrete & Continuous Dynamical Systems - B, 2014, 19 (7) : 1935-1953. doi: 10.3934/dcdsb.2014.19.1935 |
[12] |
M. Grasselli, V. Pata. Asymptotic behavior of a parabolic-hyperbolic system. Communications on Pure & Applied Analysis, 2004, 3 (4) : 849-881. doi: 10.3934/cpaa.2004.3.849 |
[13] |
Graziano Crasta, Philippe G. LeFloch. Existence result for a class of nonconservative and nonstrictly hyperbolic systems. Communications on Pure & Applied Analysis, 2002, 1 (4) : 513-530. doi: 10.3934/cpaa.2002.1.513 |
[14] |
Valery Y. Glizer. Novel Conditions of Euclidean space controllability for singularly perturbed systems with input delay. Numerical Algebra, Control & Optimization, 2020 doi: 10.3934/naco.2020027 |
[15] |
Alina Chertock, Alexander Kurganov, Mária Lukáčová-Medvi${\rm{\check{d}}}$ová, Șeyma Nur Özcan. An asymptotic preserving scheme for kinetic chemotaxis models in two space dimensions. Kinetic & Related Models, 2019, 12 (1) : 195-216. doi: 10.3934/krm.2019009 |
[16] |
Petra Csomós, Hermann Mena. Fourier-splitting method for solving hyperbolic LQR problems. Numerical Algebra, Control & Optimization, 2018, 8 (1) : 17-46. doi: 10.3934/naco.2018002 |
[17] |
Wei Liu, Pavel Krejčí, Guoju Ye. Continuity properties of Prandtl-Ishlinskii operators in the space of regulated functions. Discrete & Continuous Dynamical Systems - B, 2017, 22 (10) : 3783-3795. doi: 10.3934/dcdsb.2017190 |
[18] |
Deren Han, Zehui Jia, Yongzhong Song, David Z. W. Wang. An efficient projection method for nonlinear inverse problems with sparsity constraints. Inverse Problems & Imaging, 2016, 10 (3) : 689-709. doi: 10.3934/ipi.2016017 |
[19] |
Olena Naboka. On synchronization of oscillations of two coupled Berger plates with nonlinear interior damping. Communications on Pure & Applied Analysis, 2009, 8 (6) : 1933-1956. doi: 10.3934/cpaa.2009.8.1933 |
[20] |
Guido De Philippis, Antonio De Rosa, Jonas Hirsch. The area blow up set for bounded mean curvature submanifolds with respect to elliptic surface energy functionals. Discrete & Continuous Dynamical Systems - A, 2019, 39 (12) : 7031-7056. doi: 10.3934/dcds.2019243 |
2019 Impact Factor: 1.105
Tools
Metrics
Other articles
by authors
[Back to Top]