Nonlinearity and nontrivial solutions of fourth order semilinear elliptic equations

We consider the existence of nontrivial solutions of a fourth order semilinear elliptic boundary value problem with Dirichlet boundary condition, Δ2u + cΔu = b1[(u + 1)+ − 1] + b2u+ in Ω, where Ω is a bounded open set in RN with smooth boundary ∂Ω. The variation of linking theorem is useful to investigate them. We investigate them in six regions of (b1,b2) when λ1 < c <λ2.  2003 Elsevier Inc. All rights reserved.