Degenerate elliptic inequalities with critical growth

JOURNAL OF DIFFERENTIAL EQUATIONS

卷:232

Article

Ming Fang

关键词: critical Sobolev exponent;    variational inequality;    positive solution;    concentration compactness method;    (PS)(c) condition;   

DOI  :  10.1016/j.jde.2006.09.013

来源: Elsevier

【 摘 要 】

This article is motivated by the fact that very little is known about variational inequalities of general principal differential operators with critical growth. The concentration compactness principle of P.L. Lions [P.L. Lions, The concentration compactness principle in the calculus of variation. The limit case 1, Rev. Mat. Iberoamericana 1 (1) (1985) 145-201; P.L. Lions, The concentration compactness principle in the calculus of variation. The limit case 11, Rev. Mat. Iberoamericana 1 (2) (1985) 45-121] is a widely applied technique in the analysis of Palais-Smale sequences. For critical growth problems involving principal differential operators Laplacian or p-Laplacian, much has been accomplished in recent years, whereas very little has been done for problems involving more general main differential operators since a nonlinearity is observed between the corresponding functional I (u) and measure p introduced in the concentration compactness method. In this paper, we investigate a Leray-Lions type operator and behaviors of its (P.S.)(c) sequence. (c) 2006 Elsevier Inc. All rights reserved.

【 授权许可】

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