Perturbations from Symmetric Elliptic Boundary Value Problems

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