On the connection problem for the p-Laplacian system for potentials with several global minima

TL;DR

This paper investigates the existence of solutions to p-Laplacian systems connecting multiple minima of potentials, addressing the connection problem in various dimensions and for multiple minima.

Contribution

It extends the connection problem analysis for p-Laplacian systems to potentials with multiple global minima across different dimensions.

Findings

Existence results for systems with two minima in arbitrary dimensions.

Existence results for systems with three or more minima on the plane.

Analysis of the connection problem for complex potential landscapes.

Abstract

We study the existence of solutions to systems of ordinary differential equations that involve the p-Laplacian for potentials with several global minima. We consider the connection problem for potentials with two minima in arbitrary dimensions and with three or more minima on the plane.