Existence and multiplicity of positive weak solutions for a new class of $(p; q)$-Laplacian systems

TL;DR

This paper investigates the existence and multiplicity of positive weak solutions for a new class of $(p,q)$-Laplacian elliptic systems using sub-super solution methods, without sign restrictions on certain functions.

Contribution

It introduces new existence and multiplicity results for $(p,q)$-Laplacian systems without sign conditions, expanding the understanding of such nonlinear elliptic systems.

Findings

Existence of positive weak solutions established

Multiplicity of solutions proven under specific conditions

Examples provided to illustrate main results

Abstract

The paper is concerned with the existence of positive weak solutions for a new class of $\left( p,q\right) $-Laplacian elliptic systems in a bounded domain by means of the method of sub-super solutions. Particularly, we do not need any sign conditions for $\gamma \left( 0\right), g\left( 0\right), f\left( 0\right) $ and $h\left(0\right) $. Moreover, a multiplicity result is obtained when $\gamma \left(0\right)=g\left( 0\right)=f\left( 0\right)=h\left( 0\right)=0.$ Finally, we give some examples to verify our main results.