MULTIPLICITY OF POSITIVE SOLUTIONS FOR A CLASS OF CONCAVE-CONVEX ELLIPTIC EQUATIONS WITH CRITICAL GROWTH

被引：8

作者：

Liao, Jianfeng ^{[1
,2
]}

Pu, Yang ^{[1
,2
]}

Tang, Chunlei ^{[1
]}

机构：

[1] Southwest Univ, Sch Math & Stat, Chongqing 400715, Peoples R China

[2] China West Normal Univ, Sch Math & Informat, Nanchong 637002, Peoples R China

来源：

ACTA MATHEMATICA SCIENTIA | 2018年 / 38卷 / 02期

基金：

中国国家自然科学基金;

关键词：

Semilinear elliptic equations; critical growth; positive solutions; Nehari method; variational method; CRITICAL SOBOLEV EXPONENT; CHANGING WEIGHT FUNCTION; R-N; P-LAPLACIAN; NONLINEARITIES; EXISTENCE; PDES;

D O I：

10.1016/S0252-9602(18)30763-X

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

In this article, the following concave and convex nonlincarities elliptic equations involving critical growth is considered, {-Delta u = g(x)vertical bar u vertical bar(2*-2)u + lambda f(x)vertical bar u vertical bar(q-2)u, x is an element of Omega, u = 0, x is an element of partial derivative Omega, where Omega subset of R-N (N >= 3) is an open bounded domain with smooth boundary, 1 < q < 2, lambda > 0. 2* 2* = 2N/N-2 is the critical Sobolev exponent, f is an element of L2*/2*-q(Omega) is nonzero and nonnegative, and g is an element of C((Omega) over bar) is a positive function with k local maximum points. By the Nehari method and variational method, k +1 positive solutions are obtained. Our results complement and optimize the previous work by Lin [MR2870946, Nonlinear Anal. 75(2012) 2660-2671].

引用

页码：497 / 518

页数：22

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