Multiple solutions for elliptic problems with asymmetric nonlinearity

In this paper we establish the existence of multiple solutions for the semilinear elliptic problem −Δu = g(x,u) in Ω, u =0 on∂Ω, where Ω ⊂ RN is an open bounded domain with smooth boundary ∂Ω, g : Ω × R→R is a function of class C1 such that g(x, 0) = 0 and which is asymptotically linear at infinity with jumping nonlinearities. We use critical groups to distinguish the critical points.  2003 Elsevier Inc. All rights reserved