Qualitative properties and existence of sign changing solutions with compact support for an equation with a p-Laplace operator

TL;DR

This paper investigates radial solutions to a p-Laplace elliptic equation, establishing the existence of compactly supported, sign-changing solutions with prescribed nodes using a phase plane shooting method.

Contribution

It introduces a novel shooting method based on phase plane analysis to prove the existence of solutions with specific qualitative properties and prescribed nodal structure.

Findings

Existence of compactly supported solutions with any number of nodes.

Solutions exhibit specific qualitative properties derived from phase plane analysis.

Method applicable to a class of p-Laplace elliptic equations.

Abstract

We consider radial solutions of an elliptic equation involving the p-Laplace operator and prove by a shooting method the existence of compactly supported solutions with any prescribed number of nodes. The method is based on a change of variables in the phase plane corresponding to an asymptotic Hamiltonian system and provides qualitative properties of the solutions.