Existence and nonexistence of solutions for quasilinear elliptic equations

JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS

卷:245

Article

Montenegro, M

关键词: elliptic;    quasilinear;    degenerate;    p-Laplacian;    critical growth in the gradient;    existence and nonexistence of solution;   

DOI  :  10.1006/jmaa.1999.6697

来源: Elsevier

【 摘 要 】

In this paper we study the problem -Delta(p)u = f(x, u, del u) in Omega u = 0 on partial derivative Omega, where Omega subset of R-N is a smooth bounded domain, N greater than or equal to 2, and Delta(p)u = div(\del u\(p-2) del u) defines the p-Laplacian. We provide some necessary and sufficient conditions on f under which the problem admits a weak solution. For the case p = 2 we obtain more general conditions on f. The main ingredients are degree theory and the super-subsolution method. (C) 2000 Academic Press.

【 授权许可】

Free