Existence and multiplicity of weak solutions for a system of fourth‐order elliptic equations with combined nonlocal and indefinite source terms

This manuscript aims to investigate the existence of weak solutions for a system of partial differential equations (PDEs) described by Equation (1.2). The system consists of a set of PDEs with Leray–Lions operators and nonlinear terms. The goal is to establish the existence of at least one nontrivial weak solution and at least three weak solutions for the system. The PDEs are defined on a bounded domain in ℝN$$ {\mathrm{\mathbb{R}}}^N $$, with N≥3$$ N\ge 3 $$, and subject to appropriate boundary conditions. The system involves various parameters, functions, and growth conditions that are carefully defined throughout the paper. The study focuses on understanding the behavior and existence of solutions for this system of PDEs, which has applications in physics, engineering, and other scientific fields.