Positive Solution for a Class of Infinite Semipositone (p,q)-Laplace System - Zeditri, Sounia; Akrout, Kamel; Guefaifia, Rafik (Discontinuity, Nonlinearity, and Complexity, 2026)
In this paper we consider following (p,q)-Laplacian system $$ \left\{ \begin{aligned} & -\Delta _{p}u=\lambda l\left( x\right) u^{p-1}-f_{1}\left( u,v\right) -au^{-\alpha _{1}}v^{\beta _{2}}\ \text{in }\Omega , \\ & -\Delta _{q}v=\mu k\left( x\right) v^{q-1}-f_{2}\left( u,v\right) -bu^{\alpha _{2}}v^{-\beta _{2}}\text{ in }\Omega , \\ & u=v=0\text{ on }\partial \Omega , \end{aligned} \right. $$ where $\Omega $ is a bounded domain in $\mathbb{R}^{N}$ with smooth boundary $\partial \Omega $, $\lambda $ and $\mu $ are a positive parameters and $a,$ $b$ are a positive constant. By using the method of sub-supersolution we discuss the existence of positive solution.