On a Kirchhoff type problem in RN

JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS

卷:425

Article

Wu, Yuanze¹  Huang, Yisheng²  Liu, Zeng³ 

[1] China Univ Min & Technol, Coll Sci, Xuzhou 221116, Peoples R China

[2] Soochow Univ, Dept Math, Suzhou 215006, Peoples R China

[3] Suzhou Univ Sci & Technol, Dept Math, Suzhou 215009, Peoples R China

关键词: Kirchhoff type problem;    Nontrivial solution;    Variational method;   

DOI  :  10.1016/j.jmaa.2014.12.017

来源: Elsevier

【 摘 要 】

In this paper, we investigate the following Kirchhoff type problem: {(alpha integral(RN) (vertical bar del u vertical bar(2) + u(2)) dx + beta) (-del u + u) = vertical bar u vertical bar(p-2)u in R-N, {u is an element of H-1 (R-N), (P-alpha,P-beta) where N >= 1, 2 < p < 2* (2* = 2N/(N - 2) if N >= 3, 2* = infinity if N = 1,2) and alpha,beta are two positive parameters. By studying the decomposition of the Nehari manifold to (P-alpha,P-beta) and using the scaling technique, we give a total description on the positive solutions to (P-alpha,P-beta). We also make an observation on the sign-changing solutions to (P-alpha,P-beta) in the current paper. (C) 2014 Elsevier Inc. All rights reserved.

【 授权许可】

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