Existence and asymptotic behavior of ground states for quasilinear singular equations involving Hardy-Sobolev exponents

JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS

卷:322

Article

Alves, C. O. ; Goncalves, J. V. ; Santos, C. A.

关键词: quasilinear singular equations;    ground states;    variational methods;    lower-upper solutions;   

DOI  :  10.1016/j.jmaa.2005.09.024

来源: Elsevier

【 摘 要 】

We study the existence and decaying rate of solutions for the quasilinear problem { -Delta(p)u = rho(x)f(u) + (lambda)/(vertical bar x vertical bar theta) g(u) in R-N, u > 0 in R-N, u(x) (vertical bar x vertical bar ->infinity) -> 0, where Delta(p) stands for the p-Laplacian operator, 1 < p < N, rho: R-N -> [0, infinity) is continuous and not identically zero, lambda >= 0 is a parameter, vertical bar x vertical bar is the Euclidean norm of x, 0 <= theta <= p, f, g : [0, infinity) -> [0, infinity) are continuous and nondecreasing, f has sublinear growth and the Hardy-Sobolev exponent p(theta)* := p (N - theta)/(N - p) bounds the growth of g. We deal with variational methods and the lower and upper solutions technique. (c) 2005 Elsevier Inc. All rights reserved.

【 授权许可】

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