On a mixed cubic-superlinear non radially symmetric Schr\"odinger system - Part I: Existence and uniqueness of solutions

TL;DR

This paper investigates the existence and uniqueness of steady state solutions for a nonlinear coupled Schrödinger system with mixed cubic and superlinear nonlinearities, using variational methods on a Nehari manifold.

Contribution

It introduces a novel approach to analyze a coupled Schrödinger system with mixed nonlinearities, establishing existence and uniqueness results for steady states.

Findings

Proved existence of solutions under certain conditions.

Established uniqueness of solutions in the considered framework.

Applied variational methods on Nehari manifold for analysis.

Abstract

In this paper a nonlinear coupled Schrodinger system in the presence of mixed cubic and superlinear power laws is considered. Focus are made on the steady state solutions of the continuous system for existence and uniqueness by minimizing problem on some associated Nehari manifold.