一类二阶非线性差分方程同宿解的多解性

doi:10.6040/j.issn.1671-9352.0.2014.241

山东大学学报（理学版） ›› 2015, Vol. 50 ›› Issue (05): 51-54.doi: 10.6040/j.issn.1671-9352.0.2014.241

一类二阶非线性差分方程同宿解的多解性

孙国伟, 买阿丽

运城学院应用数学系, 山西运城 044000

收稿日期:2014-05-26 出版日期:2015-05-20 发布日期:2015-05-29
作者简介:孙国伟(1980-),男,硕士,讲师,研究方向为微分方程及其应用和数学建模及应用.E-mail:sunkanry@163.com
基金资助:
国家自然科学基金资助项目(11371313);2014年运城学院院级博士科研启动项目资助(YQ-2014011)

Multiple homoclinic solutions for second order nonlinear difference equations

SUN Guo-wei, MAI A-li

Department of Applied Mathematics, Yuncheng University, Yuncheng 044000, Shanxi, China

Received:2014-05-26 Online:2015-05-20 Published:2015-05-29

摘要/Abstract

摘要： 研究了一类二阶非线性差分方程同宿解的存在性。利用临界点理论, 在满足更一般的超线性条件下, 证明了该方程同宿解的多解性。

关键词: 差分方程, Nehari流形, 临界点理论, 同宿解

Abstract: We study the existence of homoclinic solutions for a class of second order nonlinear difference equations. Under more general superlinear conditions, we prove the multiplicity results of the equations by using critical point theory.

Key words: difference equations, Nehari manifold, critical point theory, homoclinic solutions

中图分类号:

O175.1

孙国伟, 买阿丽. 一类二阶非线性差分方程同宿解的多解性[J]. 山东大学学报（理学版）, 2015, 50(05): 51-54.

SUN Guo-wei, MAI A-li. Multiple homoclinic solutions for second order nonlinear difference equations[J]. JOURNAL OF SHANDONG UNIVERSITY(NATURAL SCIENCE), 2015, 50(05): 51-54.

参考文献

[1] GUO Zhiming, YU Jianshe. The existence of periodic and subharmonic solutions of subquadratic second order difference equations[J]. J Lond Math Soc, 2003, 68(2):419-430.
[2] GUO Zhiming, YU Jianshe. Existence of periodic and subharmonic solutions for second-order superlinear difference equations[J]. Sci China Ser A, 2003, 46(4):506-515.
[3] ZHOU Zhan, YU Jianshe, GUO Zhiming. Periodic solutions of higher-dimensional discrete systems[J]. Proc Roy Soc Edinburgh Sect A, 2004, 134(5):1013-1022.
[4] MA Manjun, GUO Zhiming. Homoclinic orbits for second order self-adjoint difference equations[J]. J Math Anal Appl, 2006, 323(1):513-521.
[5] MA Defang, ZHOU Zhan. Existence and multiplicity results of homoclinic solutions for the DNLS equations with unbounded potentials[J]. Abstra Appl Anal, 2012, 2012: 1-15.
[6] MAI Ali, ZHOU Zhan. Ground state solutions for the periodic discrete nonlinear Schrdinger equations with superlinear nonlinearities[J]. Abstr Appl Anal, 2013, 2013: 1-11.
[7] MAI Ali, ZHOU Zhan. Discrete solitons for periodic discrete nonlinear Schrdinger equations[J]. Appl Math Comput, 2013, 222:34-41.
[8] SUN Guowei. On Standing Wave solutions for discrete nonlinear Schrdinger equations[J]. Abstr Appl Anal, 2013, 2013: 1-6.
[9] IANNIZZOTTO A, TERSIAN S. Multiple homoclinic orbits for the discrete p-Laplacian via critical point theory[J]. J Math Anal Appl, 2013, 403(1):173-182.
[10] RABINOWITZ P. Minimax methods in critical point theory with applications to differential equations[M]//CBMS Regional Conference Series in Mathematics vol 65. Providence: American Mathematical Society, 1986.

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一类二阶非线性差分方程同宿解的多解性

Multiple homoclinic solutions for second order nonlinear difference equations

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