Existence of a positive solution for nonlinear Schrödinger equations with general nonlinearity

Abstract

We study the following nonlinear Schrödinger equations: -Δu+V(x)u=f(u)inℝN.$ - \Delta u + V(x) u = f(u) \quad \text{in } {\mathbb {R}^N}. $ The purpose of this paper is to establish the existence of a positive solution under general conditions which are weaker than the Ambrosetti–Rabinowitz condition.

Keywords

• variational method
• nonlinear schrödinger equation
• positive solution
• 35j20
• 35j61
• 49j35