没有Landesman-Lazer 型条件的拟线性强振动方程之无穷多解

数学物理学报 ›› 2012, Vol. 32 ›› Issue (4): 744-752.

没有Landesman-Lazer 型条件的拟线性强振动方程之无穷多解

饶若峰, 王雄瑞

宜宾学院数学系四川宜宾 |644007

收稿日期:2011-03-01 修回日期:2012-04-20 出版日期:2012-08-25 发布日期:2012-08-25
基金资助:
四川省教育厅(青年)自然科学基金(08ZB008)和宜宾学院重点项目(2011Z04)资助

Infinitely Many Solutions for the Resonant Quasi-linear Equation Without Landesman-Lazer Conditions

RAO Ruo-Feng, WANG Xiong-Rui

Department of Mathematics, Yibin University, Sichuan |Yibin 644007

Received:2011-03-01 Revised:2012-04-20 Online:2012-08-25 Published:2012-08-25
Supported by:
四川省教育厅(青年)自然科学基金(08ZB008)和宜宾学院重点项目(2011Z04)资助

摘要/Abstract

摘要：

椭圆型振动方程往往需要一个所谓的 Landesman-Lazer型条件假设. 但该文充分利用第一特征函数的性质以及亏格技巧在没有Landesman-Lazer 型条件假设的情况下给出了强振动方程-Δ_pu=λ₁|u|^p-2u+g(x, u) 无穷多解的存在性结论, 将一些最近结论从几个有限解的存在性推广到无穷多解的存在性结果.

关键词: p-Laplacian 算子, 形变引理, Palais-Smale 条件

Abstract:

The famous Landesman-Lazer conditions is used to be applied in solving the existent solution for elliptic resonant equations. In this paper, the author is by using the property of the space of the first eigenfunctions and the technique of genus to give an existence theorem for infinitely many solutions of the strong resonant equation -Δ_pu=λ₁|u|^p-2u+g(x, u) without any Landesman-Lazer conditions, which extends some recent results from single or several solutions to infinitely many solutions.

Key words: p-Laplacian operator, Deformation Lemma, Palais-Smale condition

中图分类号:

35J65

饶若峰, 王雄瑞. 没有Landesman-Lazer 型条件的拟线性强振动方程之无穷多解[J]. 数学物理学报, 2012, 32(4): 744-752.

RAO Ruo-Feng, WANG Xiong-Rui. Infinitely Many Solutions for the Resonant Quasi-linear Equation Without Landesman-Lazer Conditions[J]. Acta mathematica scientia,Series A, 2012, 32(4): 744-752.

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