Sublinear singular elliptic problems with two parameters

[摘要] We establish several existence and nonexistence results for the boundary value problem -Deltau + K(x)g(u) = lambdaf(x, it) + muh(x) in Omega, u = 0 on partial derivativeOmega, where Omega is a smooth bounded domain in R-N, lambda and mu are positive parameters, It is a positive function, while f has a sublinear growth. The main feature of this paper is that the nonlinearity g is assumed to be unbounded around the origin. Our analysis shows the importance of the role played by the decay rate of g combined with the signs of the extremal values of the potential K(x) on (Omega) over bar. The proofs are based on various techniques related to the maximum principle for elliptic equations. (C) 2003 Elsevier Science (USA). All rights reserved.

[发布日期] 2003-12-10

[关键词] singular elliptic equation;sublinear boundary value problem;maximum principle;positive solution;extremal solutions