Nontrivial solutions for Neumann problems with an indefinite linear part

In this paper, we consider a semilinear Neumann problem with an indefinite linear part and a Carathéodory nonlinearity which is superlinear near infinity and near zero, but does not satisfy the Ambrosetti–Rabinowitz condition. Using an abstract existence theorem for C1-functions having a local linking at the origin, we establish the existence of at least one nontrivial smooth solution.