A variational approach to multiplicity in elliptic problems near resonance

We consider the nonlinear elliptic problem +/-(Delta u + lambda u) + f(x, u) = h(x) in Omega, u = 0 on partial derivative Omega, where Omega is a bounded smooth domain in R-N lambda is near the first eigenvalue and h(x) is orthogonal to the first eigenfunction. We give some conditions of existence of positive solutions and of multiple solutions in terms of the primitive off with respect to u.