Vanishing properties of sign changing solutions to p-Laplace type equations in the plane

TL;DR

This paper investigates the vanishing properties of sign-changing solutions to p-Laplacian and Fučík spectrum problems in the plane, providing insights into their behavior and characteristics.

Contribution

It introduces a method applicable in the plane to analyze vanishing properties of sign-changing solutions for nonlinear eigenvalue problems involving the p-Laplacian.

Findings

Identifies vanishing properties of solutions in the plane

Provides a new analytical approach for sign-changing solutions

Enhances understanding of Fučík spectrum in planar domains

Abstract

We study the nonlinear eigenvalue problem for the p-Laplacian, and more general problem constituting the Fucik spectrum. We are interested in some vanishing properties of sign changing solutions to these problems. Our method is applicable in the plane.