Bifurcation results for quasi-linear operators from the Fucik spectrum of the Laplacian

TL;DR

This paper studies bifurcation phenomena for quasi-linear elliptic operators related to the Fučík spectrum of the Laplacian, revealing how solutions emerge from trivial states and infinity.

Contribution

It provides new bifurcation results for the $(p,2)$-Laplace operator within the Fučík spectrum framework, extending understanding of eigenvalue problems for quasi-linear operators.

Findings

Bifurcation from trivial solutions identified

Bifurcation from infinity established

Results extend spectral analysis of quasi-linear operators

Abstract

In this paper, we analyze an eigenvalue problem for a quasi-linear elliptic operators involving Dirichlet boundary condition in an open smooth bounded set of $\mathbb{R}^N$. We investigate a bifurcation results (from trivial solution and from infinity) of an eigenvalue problem involving the $(p,2)$-Laplace operator, from the Fu\v cik spectrum of the Laplacian.