Solutions to Semilinear Elliptic Problems with Combined Nonlinearities

We are concerned with the following nonlinear Dirichlet problem: , where Ω is a bounded smooth domain in RN (N 1) and h(x) L∞(Ω), 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.