Perturbations from symmetric elliptic boundary value problems

Abstract

We study the multiplicity of solutions for the elliptic problem where E is a parameter, Ω is a smooth bounded domain in ℝN, f ε C(̄W × ℝ), f(x, t) is odd with respect to t, and g ε C(̄W × ℝ). Under suitable conditions only on f, we prove that for any j ε ℕ there exists Ej > 0 such that if ε ≤Ej then the above problem possesses at least j distinct solutions. © 2002 Elsevier Science (USA).