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

被引：80
|
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
收藏
页码：2216 / 2239
页数：24
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