Solutions to semilinear elliptic problems with combined nonlinearities

[摘要] We are concerned with the following nonlinear Dirichlet problem: [GRAPHICS] where Omega is a bounded smooth domain in R-N (N greater than or equal to 1) and h(x) is an element of L-infinity(Omega), f(x, s) is asymptotically linear with respect to s at infinity. By a variant version of Mountain Pass Theorem, we prove that there exist at least two nonnegative solutions under suitable assumptions on f(x, s). Our methods also work for the cases where f(x, s) is superlinear or linear in s. (C) 2002 Elsevier Science (USA).

[发布日期] 2002-10-10

[关键词] elliptic problem;sublinear;superlinear;asymptotically linear;Mountain Pass Theorem