WU Fan,DONG Yuwei,HOU Chengmin*.Multiple homoclinic solutions for the partial difference equations with p-Laplacian operator[J].Journal of Yanbian University,2016,42(01):1-6.
带有p-Laplacian算子的四阶偏差分方程的多重同宿解
- Title:
- Multiple homoclinic solutions for the partial difference equations with p-Laplacian operator
- 关键词:
- 偏差分方程; p -Laplacian算子; 临界点定理; 变分法
- Keywords:
- partial difference equations; p -Laplacian operator; critical point theory; variational methods
- 分类号:
- O175.6
- 文献标志码:
- A
- 摘要:
- 考虑一类含有1个正参数的四阶p -Laplacian偏差分方程解的存在性问题.首先建立了一个变分框架,其次利用临界点定理证明了当参数充分大时该方程至少存在2个非平凡同宿解.所得结果推广了文献[4]的结果.
- Abstract:
- A class of four order p-Laplacian partial difference equation with a positive parameter is considered. We first introduce a variational framework. Second, by means of critical point theory, we prove the existence of at least two nontrivial homoclinic solutions for big enough parameter. The results of the literature [4] are generalized.
参考文献/References:
[1] Cabada A, Iannizzotto A, Tersian S. Multiple solutions for discrete boundary value problems[J]. J Math Anal Appl, 2009,356:418-428.
[2] De Coster C, Willem M. Density, spectral theory and homoclinics for singular Sturm-Liouville system[J]. J Comput Appl Math, 1994,52:45-70.
[3] Faraci F, Iannizzotto A. Multiplicity theorems for discrete boundary value problems[J]. Aequationes Math, 2007,74:111-118.
[4] Lannizzotto A, Tersian S A. Multiple homoclinic solutions for the discrete p-Laplacian via critial point theory[J]. J Math Anal Appl, 2013,403:173-182.
[5] Jiang L Q, Zhou Z. Three solutions to Dirichlet boundary value problems for p-Laplacian difference equations[J]. Adv Difference Equations, 2008,11:345916
[6] Fabian M, Habala P, Hájek P, et al. Banach Space Theory[M]. Springer, 2011.
[7] Pucci P, Serrin J. A mountain pass theorem[J]. J Differential Equations, 1985,60:142-149.
[8] 司文艺,侯成敏.一类四阶偏差分方程边值问题解的存在性[J].延边大学学报(自然科学版),2010,36(1):1-6.
相似文献/References:
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LIN Qiutong,GE Qi*.Existence of multiple positive solutions for a class of boundaryvalue problems of fractional q -differences with p -Laplacian[J].Journal of Yanbian University,2018,44(01):199.
[2]董强,侯成敏*.具有p -Laplacian算子的delta-nabla分数阶
差分边值问题正解的存在性[J].延边大学学报(自然科学版),2019,45(04):283.
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备注/Memo
收稿日期: 2016-02-26 *通信作者: 侯成敏(1963—),女,教授,研究方向为微分方程理论及应用. 基金项目: 国家自然科学基金资助项目(11161049); 吉林省教育厅“十二五”科技项目(吉教科合字[2014]第20号)