Existence results for the general Schrödinger equations with a superlinear Neumann boundary value problem

Abstract

Abstract The main goal of this paper is to study the general Schrödinger equations with a superlinear Neumann boundary value problem in domains with conical points on the boundary of the bases. First the formulation and the complex form of the problem for the equations are given, and then the existence result of solutions for the above problem is proved by the complex analytic method and the fixed point index theory, where we absorb the advantages of the methods in recent works and give some improvement and development. Finally, we are also interested in the asymptotic behavior of solutions of the mentioned equation. These results generalize some previous results concerning the asymptotic behavior of solutions of non-delay systems of Schrödinger equations or of delay Schrödinger equations.

Keywords

• General Schrödinger equation
• Neumann boundary condition
• Asymptotic behavior