EXISTENCE OF MULTIPLE NONTRIVIAL SOLUTIONS FOR A p-KIRCHHOFF TYPE ELLIPTIC PROBLEM INVOLVING SIGN-CHANGING WEIGHT FUNCTIONS

被引：9

作者：

Li, Yuanxiao ^{[1
,2
]}

Mei, Ming ^{[3
,4
]}

Zhang, Kaijun ^{[1
]}

机构：

[1] NE Normal Univ, Sch Math & Stat, Changchun 130024, Peoples R China

[2] Henan Univ Technol, Coll Sci, Zhengzhou 450052, Peoples R China

[3] Champlain Coll, Dept Math, St Lambert, PQ J4P 3P2, Canada

[4] McGill Univ, Dept Math & Stat, Montreal, PQ H3A 2K6, Canada

来源：

DISCRETE AND CONTINUOUS DYNAMICAL SYSTEMS-SERIES B | 2016年 / 21卷 / 03期

基金：

加拿大自然科学与工程研究理事会;

关键词：

p-Kirchhoff type equation; sign-changing weight functions; Nehari manifold; Ekeland variational principle; truncation argument; POSITIVE SOLUTIONS; EQUATION;

D O I：

10.3934/dcdsb.2016.21.883

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

This paper deals with a p-Kirchhoff type problem involving sign changing weight functions. It is shown that under certain conditions, by means of variational methods, the existence of multiple nontrivial nonnegative solutions for the problem with the subcritical exponent are obtained. Moreover, in the case of critical exponent, we establish the existence of the solutions and prove that the elliptic equation possesses at least one nontrivial nonnegative solution.

引用

页码：883 / 908

页数：26

共 28 条

[1] ON A CLASS OF NONLOCAL ELLIPTIC PROBLEMS WITH CRITICAL GROWTH [J].

Alves, C. O. ;

Correa, F. J. S. A. ;

Figueiredo, G. M. .

DIFFERENTIAL EQUATIONS & APPLICATIONS, 2010, 2 (03) :409-417

[2]

Alves C. O., 2001, Commun. Appl. Nonlinear Anal., V8, P43

[3] Positive solutions for a quasilinear elliptic equation of Kirchhoff type [J].

Alves, CO ;

Corrêa, FJSA ;

Ma, TF .

COMPUTERS & MATHEMATICS WITH APPLICATIONS, 2005, 49 (01) :85-93

[4] A uniqueness result for a nonlocal equation of Kirchhoff type and some related open problem [J].

Anello, Giovanni .

JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS, 2011, 373 (01) :248-251

[5]

[Anonymous], 1883, Mechanik

[6] The Nehari manifold for a semilinear elliptic equation with a sign-changing weight function [J].

Brown, KJ ;

Zhang, YP .

JOURNAL OF DIFFERENTIAL EQUATIONS, 2003, 193 (02) :481-499

[7] The Nehari manifold for a Kirchhoff type problem involving sign-changing weight functions [J].

Chen, Ching-yu ;

Kuo, Yueh-cheng ;

Wu, Tsung-fang .

JOURNAL OF DIFFERENTIAL EQUATIONS, 2011, 250 (04) :1876-1908

[8] Existence results of positive solutions of Kirchhoff type problems [J].

Cheng, Bitao ;

Wu, Xian .

NONLINEAR ANALYSIS-THEORY METHODS & APPLICATIONS, 2009, 71 (10) :4883-4892

[9] Some remarks on non local elliptic and parabolic problems [J].

Chipot, M ;

Lovat, B .

NONLINEAR ANALYSIS-THEORY METHODS & APPLICATIONS, 1997, 30 (07) :4619-4627

[10]

CHIPOT M, 1992, RAIRO-MATH MODEL NUM, V26, P447

← 1 2 3 →