Unilateral global interval bifurcation theorem for $p$-Laplacian and its applications

TL;DR

This paper establishes a unilateral global bifurcation theorem for p-Laplacian problems, analyzes their spectrum, and investigates nodal solutions, advancing understanding of nonlinear differential equations.

Contribution

It introduces a new unilateral bifurcation theorem for p-Laplacian problems and applies it to spectral analysis and nodal solutions of half-quasilinear eigenvalue problems.

Findings

Established a unilateral global bifurcation theorem from interval for p-Laplacian problems

Analyzed the spectrum of half-quasilinear problems

Proved existence of nodal solutions for eigenvalue problems

Abstract

In this paper, we establish a unilateral global bifurcation result from interval for a class of $p$-Laplacian problems. By applying the above result, we study the spectrum of a class of half-quasilinear problems. Moreover, we also investigate the existence of nodal solutions for a class of half-quasilinear eigenvalue problems.