Solutions for a Nonhomogeneous Nonlinear Schroedinger Equation with Double Power Nonlinearity

TL;DR

This paper investigates the existence of solutions for a nonhomogeneous nonlinear Schrödinger equation with double power nonlinearity, demonstrating solutions under specific conditions on the potential and forcing term.

Contribution

It establishes the existence of two solutions for the equation when the forcing term is small and the potential is negative, considering the double power nonlinear behavior.

Findings

Two solutions exist when g is sufficiently small and V < 0.

Solutions are proven under the condition lim_{x→∞} V(x) = 0.

The nonlinear term exhibits double power behavior.

Abstract

We consider the problem -\Delta u+V(x)u = f'(u)+g(x) in RN, under the assumption limx \rightarrow \infty V (x) = 0, and with the non linear term f with a double power behavior. We prove the existence two solutions when g is sufficiently small and V < 0.