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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. Google Scholar |
[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.
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.
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.
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.
|
[6] |
A. Lasota and Z. Opial, Sur les solutions périodiques des equations differentielles ordinaires,, Ann. Polon. Math., 16 (1964), 69.
|
[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.
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.
|
[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.
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.
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.
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.
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.
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.
doi: 10.2307/2043477. |
[15] |
M. R. Zhang, An abstract result on asympotitically positively homogeneous differential equations,, J. Math. Anal. Appl., 209 (1997), 291.
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. Google Scholar |
[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.
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.
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.
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.
|
[6] |
A. Lasota and Z. Opial, Sur les solutions périodiques des equations differentielles ordinaires,, Ann. Polon. Math., 16 (1964), 69.
|
[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.
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.
|
[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.
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.
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.
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.
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.
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.
doi: 10.2307/2043477. |
[15] |
M. R. Zhang, An abstract result on asympotitically positively homogeneous differential equations,, J. Math. Anal. Appl., 209 (1997), 291.
doi: 10.1006/jmaa.1997.5383. |
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