Schrödinger equation with asymptotically linear nonlinearities


Amel El-Abed, Abir Amor Ben Ali, Makkia Dammak




In this paper, we investigate a quasilinear Schrödinger problem under Dirichlet boundary condition in a regular domain with asymptotically linear nonlinearities. We use Cerami version of the mountain pass theorem to prove the existence of solution without using the Ambrosetti-Rabionovitz condition or any of its refinements. Then, we prove that the same techniques work when the nonlinearity is superlinear and subcritical at infinity