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

Abstract

In this paper, we study the existence and asymptotic behaviors of ground state solutions to a fourth-order nonlinear Schrödinger equation with mass-critical exponent, where the fourth-order term appears as a perturbation with ε>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 ε→0+. The main ingredients of the proofs are some energy estimate arguments. Our results improve somewhat the ones in the existing reference.