The existence and multiplicity of solutions for general quasi-linear elliptic equations with sub-cubic nonlinearity

TL;DR

This paper investigates the existence and multiplicity of solutions for a broad class of quasi-linear Schrödinger equations with sub-cubic nonlinearities, introducing a novel perturbation method to handle these nonlinearities.

Contribution

It presents a new perturbation approach specifically designed for sub-cubic nonlinearities in quasi-linear Schrödinger equations, expanding the understanding of solution multiplicity.

Findings

Established existence of solutions under new conditions

Proved multiplicity results for the equations studied

Developed a novel perturbation technique for sub-cubic nonlinearities

Abstract

We consider the existence and multiplicity of solutions for a class of quasi-linear Schr\"{o}dinger equations which include the modified nonlinear Schr\"{o}dinger equations. A new perturbation approach is used to treat the sub-cubic nonlinearity.