Bifurcation results for nonlinear eigenvalue problems involving the (p,q)-Laplace operator

TL;DR

This paper investigates bifurcation phenomena and multiple solutions in nonlinear eigenvalue problems involving the (p,q)-Laplace operator, using variational methods to analyze solution structures.

Contribution

It provides new bifurcation results from trivial solutions and infinity, and establishes the existence of multiple solutions for the nonlinear eigenvalue problem.

Findings

Bifurcation from trivial solutions identified

Bifurcation from infinity demonstrated

Multiple solutions established via variational methods

Abstract

In this paper, we analyze an eigenvalue problem for nonlinear elliptic operators involving homogeneous Dirichlet boundary conditions in a open smooth bounded domain. We prove bifurcation results from trivial solutions and from infinity for the considered nonlinear eigenvalue problem. We also show the existence of multiple solutions of the nonlinear problem using variational methods.