Multiple Sign-Changing Solutions for Quasilinear Elliptic Equations via Perturbation Method

被引：86

作者：

Liu, Jia-Quan ^{[1
]}

Liu, Xiang-Qing ^{[2
]}

Wang, Zhi-Qiang ^{[3
,4
,5
]}

机构：

[1] Peking Univ, Sch Math Sci, LMAM, Beijing 100871, Peoples R China

[2] Yunnan Normal Univ, Dept Math, Kunming, Peoples R China

[3] Nankai Univ, Chern Inst Math, Tianjin 300071, Peoples R China

[4] Nankai Univ, LPMC, Tianjin 300071, Peoples R China

[5] Utah State Univ, Dept Math & Stat, Logan, UT 84322 USA

来源：

COMMUNICATIONS IN PARTIAL DIFFERENTIAL EQUATIONS | 2014年 / 39卷 / 12期

关键词：

Multiple sign-changing solutions; p-Laplacian regularization; Quasilinear equations; SCHRODINGER-EQUATIONS; SOLITON-SOLUTIONS; EXISTENCE;

D O I：

10.1080/03605302.2014.942738

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

We consider existence and multiplicity of sign-changing solutions for a class of quasilinear problems which has received considerable attention in the past, including the so called Modified Nonlinear Schrodinger Equations. We develop a new variational approach to treat this class of quasilinear equations by proposing a p-Laplacian regularization process. By establishing necessary estimates we show the solutions to the perturbation problems converge in a sense to solutions of the original problems. We show that the new approach is especially effective for dealing with issues of multiple solutions and sign-changing solutions.

引用

页码：2216 / 2239

页数：24

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