Three weak solutions for a $(p, q)$-Schr\"{o}dinger-Kirchhoff type equation

TL;DR

This paper proves the existence of three weak solutions for a $(p, q)$-Schr"{o}dinger-Kirchhoff equation with a positive potential, using variational methods under specific conditions.

Contribution

It introduces a novel application of variational techniques to establish multiple solutions for a complex nonlinear PDE involving $(p, q)$-Laplacian operators.

Findings

Established existence of three weak solutions

Applied variational methods to a nonlinear PDE

Extended results to equations with positive potentials

Abstract

In this manuscript, we investigate a $(p, q)$-Schr\"{o}dinger-Kirchhoff equation involving a continuous positive potential that meets the del Pino-Felmer type conditions. Using Recceri's classical variational approach, we prove the existence of three weak solutions.