Biharmonic problem with indefinite asymptotically linear nonlinearity

In this paper, boundary fourth order semilinear elliptic problems involving nonnegative weight functions are investigated with indefinite asymptotically linear nonlinearities. Using the variational method, we prove the existence of nontrivial solutions without use of the Ambrosetti-Rabionovitz condition or any one of its replacements. When the nonlinearities are superlinear at infinity, a suitable condition is added in order to use the same techniques to prove the existence of solutions.