Existence and Non-Existence Criteria for Solutions of a Schr\"odinger Quasilinear System type

TL;DR

This paper investigates conditions under which solutions exist or do not exist for a class of quasilinear elliptic systems, including radial and non-radial solutions, using analytical methods.

Contribution

It provides new existence and non-existence criteria for solutions of coupled quasilinear elliptic systems, including symmetric and non-symmetric cases.

Findings

Established criteria for existence of radial solutions.

Derived conditions for non-existence of solutions.

Constructed non-radial solutions using lower and upper solution methods.

Abstract

In this paper we analyze the existence of large positive radial solutions to some quasilinear elliptic systems. Also, a non-radially symmetric solution is obtained by using a lower and upper solution method. The equations are coupled by functions which are increasing with respect to all the variables.