Entire solutions to a quasilinear purely critical competitive system

TL;DR

This paper proves the existence of fully nontrivial solutions with nonnegative components for a critical competitive system involving the p-Laplacian, and shows infinitely many nodal solutions for the associated critical equation.

Contribution

It establishes the existence of solutions for a critical p-Laplacian system and demonstrates infinitely many solutions for the critical equation, advancing understanding of nonlinear PDEs.

Findings

Existence of a fully nontrivial nonnegative solution for the system.

Infinitely many nodal solutions for the critical p-Laplacian equation.

Solutions are established in the context of purely critical nonlinear terms.

Abstract

We establish the existence of a fully nontrivial solution with nonnegative components for a weakly coupled competitive system for the $p$-Laplacian in $\mathbb{R}^N$ whose nonlinear terms are purely critical. We also show that the purely critical equation for the $p$-Laplacian in $\mathbb{R}^N$ has infinitely many nodal solutions.