Nonresonance Conditions on the Potential for a Semilinear Elliptic Problem

We prove the solvability of the Dirichlet problem [formula], for every given h, under the following set of assumptions: [formula] and [formula] and [formula]. Here, λm and λm + 1 denote two consecutive higher eigenvalues of −Δ on H10(Ω) and G is the potential of g. Similar results are also obtained in the case where the nonlinearity interacts with the first eigenvalue λ1.