Multiplicity of positive solutions for the Kirchhoff-type equations with critical exponent in RN

被引：13

作者：

Miyagaki, O. H. ^{[1
]}

Paes-Leme, L. C. ^{[2
]}

Rodrigues, B. M. ^{[2
]}

机构：

[1] Univ Fed Juiz de Fora, Dept Matemat, BR-36036000 Juiz De Fora, MG, Brazil

[2] Univ Fed Ouro Preto, Dept Matemat, BR-35400000 Ouro Preto, MG, Brazil

来源：

COMPUTERS & MATHEMATICS WITH APPLICATIONS | 2018年 / 75卷 / 09期

关键词：

Kirchhoff-type; Variational methods; Critical exponents; p-Laplacian; CRITICAL GROWTH; ELLIPTIC-EQUATIONS; EXISTENCE;

D O I：

10.1016/j.camwa.2018.01.041

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

In this work we study the existence and multiplicity of solutions to the following Kirchhoff-type problem with critical nonlinearity in R-N {-(a + b integral(RN) vertical bar del u vertical bar(p)dx) del(p)u = mu uP*(-1) + lambda f(x, u); x is an element of R-N, u is an element of D-1,D-P (R-N), where N >= 2p,mu,lambda,a,b > 0 and the nonlinearity f(x, u) satisfies certain subcritical growth conditions. By using topological and variational methods, infinitely many positive solutions are obtained. (C) 2018 Elsevier Ltd. All rights reserved.

引用

页码：3201 / 3212

页数：12

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