Perturbations from symmetric elliptic boundary value problems

We study the Multiplicity Of Solutions for the elliptic problem -Deltau = f(x,u) + eg(x,u) in Omega and u = 0 on partial derivativeOmega, where epsilon is a parameter, Omega is a smooth bounded domain in R-N, f is an element of C((Ω) over bar x R), f(x, t) is odd with respect to t, and y is an element of C((Ω) over bar x R). Under suitable conditions only on f, we prove that for any j is an element of N there exists epsilon(j) > 0 such that if \epsilon\ less than or equal to epsilon(j) then the above problem possesses at least j distinct solutions. (C) 2002 Elsevier Science (USA).