Positive least energy solutions for a coupled Schrodinger system with critical exponent

JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS

卷:417

Article

Ye, Hongyu¹  Peng, Yanfang² 

[1] Cent China Normal Univ, Sch Math & Stat, Wuhan 430079, Peoples R China

[2] Guizhou Normal Univ, Dept Math & Comp Sci, Guiyang 550001, Peoples R China

关键词: Coupled Brezis-Nirenberg problem;    Positive least energy solutions;    Critical exponents;    Variational methods;   

DOI  :  10.1016/j.jmaa.2014.03.028

来源: Elsevier

【 摘 要 】

In this paper, we consider the following coupled Schrodinger system with doubly critical exponents, which can be seen as a counterpart of the Brezis-Nirenberg problem: {-Delta u + lambda(1)u = mu(1)u(5) + beta u(2)v(3), x is an element of Omega, -Delta v + lambda(2)v = mu(2)v(5) + beta v(2)u(3), x is an element of Omega, u > 0, v > 0, x is an element of Omega, u=v=0, x is an element of partial derivative Omega, where Omega subset of R-3 is a smooth bounded domain, lambda(1), lambda(2) < 0, mu(1), mu(2) > 0 and beta > 0. Under certain conditions on lambda(1), lambda(2) and beta, we show that this problem has at least one positive least energy solution. (C) 2014 Published by Elsevier Inc.

【 授权许可】

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