Infinitely many solutions for quasilinear elliptic equations involving (p, q)-Laplacian in R

被引：4

作者：

Teng, Kaimin ^{[1
]}

Zhang, Chao ^{[2
]}

机构：

[1] Taiyuan Univ Technol, Dept Math, Taiyuan 030024, Shanxi, Peoples R China

[2] Harbin Inst Technol, Dept Math, Harbin 150001, Peoples R China

来源：

NONLINEAR ANALYSIS-REAL WORLD APPLICATIONS | 2016年 / 32卷

基金：

山西省青年科学基金;

关键词：

Quasilinear Schrodinger equation; Soliton solution; Infinitely many solutions; (p; q)-Laplacian; REACTION-DIFFUSION EQUATIONS; SCHRODINGER-EQUATIONS; SOLITON-SOLUTIONS; POSITIVE SOLUTIONS; Q-LAPLACIAN; EXISTENCE;

D O I：

10.1016/j.nonrwa.2016.04.008

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

In this paper, under some superquadratic conditions made on the nonlinearity f, we use variational approaches to establish the existence of infinitely many solutions to quasilinear elliptic equations with (p, q)-Laplacian -L(p)u - L(q)u + a(x)vertical bar u vertical bar(p-2)u + b(x)vertical bar u vertical bar(q-2)u = f (x, u) in R, where 1 < q < p, L(p)u = vertical bar u'vertical bar(p-2)u') + (vertical bar u(2))'vertical bar(p-2)(u(2))')'u, L(q)u = vertical bar u'vertical bar(q-2)u') + (vertical bar u(2))'vertical bar(q-2)(u(2))')'u. (C) 2016 Elsevier Ltd. All rights reserved.

引用

页码：242 / 259

页数：18

共 29 条

[1] Non-autonomous perturbations for a class of quasilinear elliptic equations on R [J].

Alves, M. J. ;

Carriao, P. C. ;

Miyagaki, O. H. .

JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS, 2008, 344 (01) :186-203

[2]

Ambrosetti A, 2003, DISCRETE CONT DYN-A, V9, P55

[3]

[Anonymous], 1997, Minimax theorems

[4]

[Anonymous], 1986, C BOARD MATH SCI

[5] Soliton like solutions of a Lorentz invariant equation in dimension 3 [J].

Benci, V ;

Fortunato, D ;

Pisani, L .

REVIEWS IN MATHEMATICAL PHYSICS, 1998, 10 (03) :315-344

[6]

Borovskii A. V., 1993, Journal of Experimental and Theoretical Physics, V77, P562

[7]

Brezis H, 2010, SOBOLEV SPACES PARTI

[8] Existence of a nontrivial solution for the (p, q)-Laplacian in RN without the Ambrosetti-Rabinowitz condition [J].

Chaves, Marcio Fialho ;

Ercole, Grey ;

Miyagaki, Olimpio Hiroshi .

NONLINEAR ANALYSIS-THEORY METHODS & APPLICATIONS, 2015, 114 :133-141

[9] Multiple positive solutions to a class of modified nonlinear Schrodinger equations [J].

Chen, Jianqing .

JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS, 2014, 415 (02) :525-542

[10] On the stationary solutions of generalized reaction diffusion equations with p&q-Laplacian [J].

Cherfils, L ;

Il'Yasov, Y .

COMMUNICATIONS ON PURE AND APPLIED ANALYSIS, 2005, 4 (01) :9-22

← 1 2 3 →