Existence and Asymptotic Behaviors of Ground States for a Fourth-Order Nonlinear Schrodinger Equations with a Potential

In this paper, we study the existence and asymptotic behaviors of ground state solutions to a fourth-order nonlinear Schrodinger equation with mass-critical exponent, where the fourth-order term appears as a perturbation with epsilon > 0. By considering a constrained variational problem, we first establish the existence of ground state solutions. Then, we prove the asymptotic behaviors of the solutions as epsilon -> 0(+). The main ingredients of the proofs are some energy estimate arguments. Our results improve somewhat the ones in the existing reference.