On multiplicity of solutions of Dirichlet problem for uniformly elliptic operator equations

In the present paper, the following Dirichlet problem A(u) = f (x,u), in Ω, u = 0, on ∂Ω, is studied and four new multiplicity results of solutions are obtained, where Ω ⊂ RN is a bounded domain, N 1 and Au=− N i,j=1 Di aij (x)Dj u +c(x)u, aij (x) = aji(x) ∈ c1(Ω), i, j = 1, 2, . . . , N, c(x) ∈ C(Ω), c(x) 0 and there isγ >0 such that N i,j=1 aij (x)ξiξj γ |ξ |2, ∀x ∈ Ω, ξ ∈ RN. © 2005 Elsevier Inc. All rights reserved