Nodal solutions for a supercritical semilinear problem with variable exponent

被引：24

作者：

Cao, Daomin ^{[1
,2
]}

Li, Shuanglong ^{[2
]}

Liu, Zhongyuan ^{[3
]}

机构：

[1] Guangzhou Univ, Sch Math & Informat Sci, Guangzhou 510405, Guangdong, Peoples R China

[2] Chinese Acad Sci, Acad Math & Syst Sci, Beijing 100190, Peoples R China

[3] Henan Univ, Sch Math & Stat, Kaifeng 475004, Henan, Peoples R China

来源：

CALCULUS OF VARIATIONS AND PARTIAL DIFFERENTIAL EQUATIONS | 2018年 / 57卷 / 02期

关键词：

LINEAR ELLIPTIC-EQUATIONS; BOUNDARY-VALUE-PROBLEMS; EXISTENCE;

D O I：

10.1007/s00526-018-1305-2

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

In this paper, we are concerned with the following nonlinear supercritical elliptic problem with variable exponent, {- Delta u = vertical bar u vertical bar(2*+vertical bar x vertical bar alpha-2)u, in B-1 (0), u = 0, on partial derivative B-1 (0), where 2* = 2N/N-2, 0 < alpha < min{N/2, N - 2}, and B-1(0) is the unit ball in R-N, N >= 3. For any k is an element of N, we find, by variational methods, a pair of nodal solutions for this problem, which has exactly k nodal points.

引用

页数：19

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