Multiple positive and sign-changing solutions of an elliptic equation with fast increasing weight and critical growth

JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS

卷:465

Article

Qian, Xiaotao^1,2,3  Chen, Jianqing^1,2 

[1] Fujian Normal Univ, Coll Math & Comp Sci, Qishan Campus, Fuzhou 350108, Fujian, Peoples R China

[2] Fujian Normal Univ, FJKLMAA, Qishan Campus, Fuzhou 350108, Fujian, Peoples R China

[3] Fujian Agr & Forestry Univ, Jinshan Coll, Fuzhou 350002, Fujian, Peoples R China

关键词: Variational methods;    Multiple positive and sign-changing solutions;    Critical problems;   

DOI  :  10.1016/j.jmaa.2018.05.058

来源: Elsevier

【 摘 要 】

We consider the following equation -div (K(x)del u) = lambda K(x)vertical bar x vertical bar(beta )vertical bar u vertical bar(q-2)u + Q(x)vertical bar u vertical bar(2*-2)u, x is an element of R-N where N >= 3, 2 < q < 2* = 2N/(N - 2), lambda > 0 is a parameter, K(x) = exp(vertical bar x vertical bar(alpha)/4), alpha >= 2, beta = (alpha - 2) (2* - q/2* - 2) and 0 <= Q(x) is an element of C(R-N). Using variational methods and delicate estimates, we establish some existence and multiplicity of positive and sign-changing solutions for the problem, provided that the maximum of Q(x) is achieved at different points. (C) 2018 Elsevier Inc. All rights reserved.

【 授权许可】

Free