-
Previous Article
Pushed traveling fronts in monostable equations with monotone delayed reaction
- DCDS Home
- This Issue
-
Next Article
Resonance problems for Kirchhoff type equations
Non-degeneracy and uniqueness of periodic solutions for $2n$-order differential equations
1. | Departamento de Matemática Aplicada, Universidad de Granada, 18071 Granada |
2. | School of Mathematics and Informatics, Henan Polytechnic University, Jiaozuo 454000, China |
3. | Dept. of Math., Zhengzhou University, Zhengzhou 450001 |
References:
[1] |
Z. B. Cheng and J. L. Ren, Periodic solutions for a fourth-order Rayleigh type $p$-Laplacian delay equation, Nonlinear Anal. TMA, 70 (2009), 516-523. |
[2] |
F. Z. Cong, Q. D. Huang and S. Y. Shi, Existence and uniqueness of periodic solution for $(2n+1)^{th}$-order differential equation, J. Math. Anal. Appl., 241 (2000), 1-9.
doi: 10.1006/jmaa.1999.6471. |
[3] |
F. Z. Cong, Periodic solutions for $2k$th order ordinary differential equations with nonresonance, Nonlinear Anal. TMA, 32 (1998), 787-793.
doi: 10.1016/S0362-546X(97)00517-8. |
[4] |
A. Fonda and J. Mawhin, Quadratic forms, weighted eigenfunctions and boundary value problems for non-linear second order ordinary differential equations, Proc. Royal Soc. Edinburgh Sect. A, 112 (1989), 145-153.
doi: 10.1017/S0308210500028213. |
[5] |
Y. Kametaka, H. Yamagishi, K. Watanabe, A. Nagai and K. Takemura, Riemann zeta function, Bernoulli polynomials and the best constant of Sobolev inequality, Sci. Math. Jpn., 65 (2007), 333-359. |
[6] |
A. Lasota and Z. Opial, Sur les solutions périodiques des equations differentielles ordinaires, Ann. Polon. Math., 16 (1964), 69-94 |
[7] |
W. Li and M. R. Zhang, Non-degeneracy and uniqueness of periodic solutions for some superlinear beam equations, Appl. Math. Lett., 22 (2009), 314-319.
doi: 10.1016/j.aml.2008.03.027. |
[8] |
G. Meng, P. Yan, X. Y. Lin and M. R. Zhang, Non-degeneracy and periodic solutions of semilinear differential equations with deviation, Adv. Nonlinear Stud., 6 (2006), 563-590. |
[9] |
R. Ortega and M. Zhang, Some optimal bounds for bifurcation values of a superlinear periodic problem, Proc. Royal Soc. Edinburgh Sect. A, 135 (2005), 119-132.
doi: 10.1017/S0308210500003796. |
[10] |
L. J. Pan, Periodic solutions for higher order differential equations with deviating argument, J. Math. Anal. Appl., 343 (2008), 904-918.
doi: 10.1016/j.jmaa.2008.01.096. |
[11] |
J. L. Ren and Z. B. Cheng, On high-order delay differential equation, Comput. Math. Appl., 57 (2009), 324-331.
doi: 10.1016/j.camwa.2008.10.071. |
[12] |
J. L. Ren and Z. B. Cheng, Periodic solutions for generalized high-order neutral differential equation in the critical case, Nonlinear Anal., 71 (2009), 6182-6193.
doi: 10.1016/j.na.2009.06.011. |
[13] |
K. Wang and S. P. Lu, On the existence of periodic solutions for a kind of high-order neutral functional differential equation, J. Math. Anal. Appl., 326 (2007), 1161-1173.
doi: 10.1016/j.jmaa.2006.03.078. |
[14] |
J. R. Ward, Asymptotic conditions for periodic solutions of ordinary differential equations, Proc. Amer. Math. Soc., 81 (1981), 415-420.
doi: 10.2307/2043477. |
[15] |
M. R. Zhang, An abstract result on asympotitically positively homogeneous differential equations, J. Math. Anal. Appl., 209 (1997), 291-298.
doi: 10.1006/jmaa.1997.5383. |
show all references
References:
[1] |
Z. B. Cheng and J. L. Ren, Periodic solutions for a fourth-order Rayleigh type $p$-Laplacian delay equation, Nonlinear Anal. TMA, 70 (2009), 516-523. |
[2] |
F. Z. Cong, Q. D. Huang and S. Y. Shi, Existence and uniqueness of periodic solution for $(2n+1)^{th}$-order differential equation, J. Math. Anal. Appl., 241 (2000), 1-9.
doi: 10.1006/jmaa.1999.6471. |
[3] |
F. Z. Cong, Periodic solutions for $2k$th order ordinary differential equations with nonresonance, Nonlinear Anal. TMA, 32 (1998), 787-793.
doi: 10.1016/S0362-546X(97)00517-8. |
[4] |
A. Fonda and J. Mawhin, Quadratic forms, weighted eigenfunctions and boundary value problems for non-linear second order ordinary differential equations, Proc. Royal Soc. Edinburgh Sect. A, 112 (1989), 145-153.
doi: 10.1017/S0308210500028213. |
[5] |
Y. Kametaka, H. Yamagishi, K. Watanabe, A. Nagai and K. Takemura, Riemann zeta function, Bernoulli polynomials and the best constant of Sobolev inequality, Sci. Math. Jpn., 65 (2007), 333-359. |
[6] |
A. Lasota and Z. Opial, Sur les solutions périodiques des equations differentielles ordinaires, Ann. Polon. Math., 16 (1964), 69-94 |
[7] |
W. Li and M. R. Zhang, Non-degeneracy and uniqueness of periodic solutions for some superlinear beam equations, Appl. Math. Lett., 22 (2009), 314-319.
doi: 10.1016/j.aml.2008.03.027. |
[8] |
G. Meng, P. Yan, X. Y. Lin and M. R. Zhang, Non-degeneracy and periodic solutions of semilinear differential equations with deviation, Adv. Nonlinear Stud., 6 (2006), 563-590. |
[9] |
R. Ortega and M. Zhang, Some optimal bounds for bifurcation values of a superlinear periodic problem, Proc. Royal Soc. Edinburgh Sect. A, 135 (2005), 119-132.
doi: 10.1017/S0308210500003796. |
[10] |
L. J. Pan, Periodic solutions for higher order differential equations with deviating argument, J. Math. Anal. Appl., 343 (2008), 904-918.
doi: 10.1016/j.jmaa.2008.01.096. |
[11] |
J. L. Ren and Z. B. Cheng, On high-order delay differential equation, Comput. Math. Appl., 57 (2009), 324-331.
doi: 10.1016/j.camwa.2008.10.071. |
[12] |
J. L. Ren and Z. B. Cheng, Periodic solutions for generalized high-order neutral differential equation in the critical case, Nonlinear Anal., 71 (2009), 6182-6193.
doi: 10.1016/j.na.2009.06.011. |
[13] |
K. Wang and S. P. Lu, On the existence of periodic solutions for a kind of high-order neutral functional differential equation, J. Math. Anal. Appl., 326 (2007), 1161-1173.
doi: 10.1016/j.jmaa.2006.03.078. |
[14] |
J. R. Ward, Asymptotic conditions for periodic solutions of ordinary differential equations, Proc. Amer. Math. Soc., 81 (1981), 415-420.
doi: 10.2307/2043477. |
[15] |
M. R. Zhang, An abstract result on asympotitically positively homogeneous differential equations, J. Math. Anal. Appl., 209 (1997), 291-298.
doi: 10.1006/jmaa.1997.5383. |
[1] |
Genni Fragnelli, Jerome A. Goldstein, Rosa Maria Mininni, Silvia Romanelli. Operators of order 2$ n $ with interior degeneracy. Discrete and Continuous Dynamical Systems - S, 2020, 13 (12) : 3417-3426. doi: 10.3934/dcdss.2020128 |
[2] |
Robert Magnus, Olivier Moschetta. The non-linear Schrödinger equation with non-periodic potential: infinite-bump solutions and non-degeneracy. Communications on Pure and Applied Analysis, 2012, 11 (2) : 587-626. doi: 10.3934/cpaa.2012.11.587 |
[3] |
Xiaocai Wang, Junxiang Xu. Gevrey-smoothness of invariant tori for analytic reversible systems under Rüssmann's non-degeneracy condition. Discrete and Continuous Dynamical Systems, 2009, 25 (2) : 701-718. doi: 10.3934/dcds.2009.25.701 |
[4] |
Lipeng Duan, Jun Yang. On the non-degeneracy of radial vortex solutions for a coupled Ginzburg-Landau system. Discrete and Continuous Dynamical Systems, 2021, 41 (10) : 4767-4790. doi: 10.3934/dcds.2021056 |
[5] |
Dongfeng Zhang, Junxiang Xu. On elliptic lower dimensional tori for Gevrey-smooth Hamiltonian systems under Rüssmann's non-degeneracy condition. Discrete and Continuous Dynamical Systems, 2006, 16 (3) : 635-655. doi: 10.3934/dcds.2006.16.635 |
[6] |
Mark Lewis, Daniel Offin, Pietro-Luciano Buono, Mitchell Kovacic. Instability of the periodic hip-hop orbit in the $2N$-body problem with equal masses. Discrete and Continuous Dynamical Systems, 2013, 33 (3) : 1137-1155. doi: 10.3934/dcds.2013.33.1137 |
[7] |
Zhongjie Liu, Duanzhi Zhang. Brake orbits on compact symmetric dynamically convex reversible hypersurfaces on $ \mathbb{R}^\text{2n} $. Discrete and Continuous Dynamical Systems, 2019, 39 (7) : 4187-4206. doi: 10.3934/dcds.2019169 |
[8] |
Paolo Caldiroli. Radial and non radial ground states for a class of dilation invariant fourth order semilinear elliptic equations on $R^n$. Communications on Pure and Applied Analysis, 2014, 13 (2) : 811-821. doi: 10.3934/cpaa.2014.13.811 |
[9] |
Carmen Cortázar, Marta García-Huidobro, Pilar Herreros, Satoshi Tanaka. On the uniqueness of solutions of a semilinear equation in an annulus. Communications on Pure and Applied Analysis, 2021, 20 (4) : 1479-1496. doi: 10.3934/cpaa.2021029 |
[10] |
Thierry Horsin, Peter I. Kogut, Olivier Wilk. Optimal $L^2$-control problem in coefficients for a linear elliptic equation. II. Approximation of solutions and optimality conditions. Mathematical Control and Related Fields, 2016, 6 (4) : 595-628. doi: 10.3934/mcrf.2016017 |
[11] |
Thierry Horsin, Peter I. Kogut. Optimal $L^2$-control problem in coefficients for a linear elliptic equation. I. Existence result. Mathematical Control and Related Fields, 2015, 5 (1) : 73-96. doi: 10.3934/mcrf.2015.5.73 |
[12] |
Nikos I. Karachalios, Athanasios N Lyberopoulos. On the dynamics of a degenerate damped semilinear wave equation in \mathbb{R}^N : the non-compact case. Conference Publications, 2007, 2007 (Special) : 531-540. doi: 10.3934/proc.2007.2007.531 |
[13] |
Carmen Cortázar, Marta García-Huidobro, Pilar Herreros. On the uniqueness of bound state solutions of a semilinear equation with weights. Discrete and Continuous Dynamical Systems, 2019, 39 (11) : 6761-6784. doi: 10.3934/dcds.2019294 |
[14] |
Lei Liu, Li Wu. Multiplicity of closed characteristics on $ P $-symmetric compact convex hypersurfaces in $ \mathbb{R}^{2n} $. Discrete and Continuous Dynamical Systems, 2021, 41 (6) : 2635-3652. doi: 10.3934/dcds.2020378 |
[15] |
Zhiming Guo, Zhi-Chun Yang, Xingfu Zou. Existence and uniqueness of positive solution to a non-local differential equation with homogeneous Dirichlet boundary condition---A non-monotone case. Communications on Pure and Applied Analysis, 2012, 11 (5) : 1825-1838. doi: 10.3934/cpaa.2012.11.1825 |
[16] |
Avadhesh Kumar, Ankit Kumar, Ramesh Kumar Vats, Parveen Kumar. Approximate controllability of neutral delay integro-differential inclusion of order $ \alpha\in (1, 2) $ with non-instantaneous impulses. Evolution Equations and Control Theory, 2021 doi: 10.3934/eect.2021058 |
[17] |
Ruofei Yao, Yi Li, Hongbin Chen. Uniqueness of positive radial solutions of a semilinear elliptic equation in an annulus. Discrete and Continuous Dynamical Systems, 2019, 39 (3) : 1585-1594. doi: 10.3934/dcds.2018122 |
[18] |
C. Cortázar, Marta García-Huidobro. On the uniqueness of ground state solutions of a semilinear equation containing a weighted Laplacian. Communications on Pure and Applied Analysis, 2006, 5 (4) : 813-826. doi: 10.3934/cpaa.2006.5.813 |
[19] |
C. Cortázar, Marta García-Huidobro. On the uniqueness of ground state solutions of a semilinear equation containing a weighted Laplacian. Communications on Pure and Applied Analysis, 2006, 5 (1) : 71-84. doi: 10.3934/cpaa.2006.5.71 |
[20] |
Tomás Caraballo, María J. Garrido–Atienza, Björn Schmalfuss, José Valero. Asymptotic behaviour of a stochastic semilinear dissipative functional equation without uniqueness of solutions. Discrete and Continuous Dynamical Systems - B, 2010, 14 (2) : 439-455. doi: 10.3934/dcdsb.2010.14.439 |
2020 Impact Factor: 1.392
Tools
Metrics
Other articles
by authors
[Back to Top]