On the existence and regularity of vector solutions for quasilinear systems with linear coupling

TL;DR

This paper investigates the existence, regularity, and asymptotic behavior of vector solutions for linearly coupled quasilinear p-Laplacian systems using variational methods, providing new insights into solution structures.

Contribution

It establishes the existence and regularity of solutions for coupled p-Laplacian systems and analyzes their asymptotic behavior as the coupling parameter approaches zero.

Findings

Existence of two pairs of nontrivial solutions

Regularity results for solutions

Asymptotic analysis as coupling tends to zero

Abstract

We study a class of linearly coupled system of quasilinear equations. Under some assumptions on the nonlinear terms, we establish some results about the existence and regularity of vector solutions for the p-Laplacian systems by using variational methods. In particular, we get two pairs of nontrivial solutions. We also study their different asymptotic behavior of solutions as the coupling parameter tends to zero.