A Weak Solution for a Nonlinear Fourth-Order Elliptic System with Variable Exponent Operators and Hardy Potential - Khaled Kefi; Mohamad M. Al-Shomrani (Mathematics)
In this paper, we investigate the existence of at least one weak solution for a nonlinear fourth-order elliptic system involving variable exponent biharmonic and Laplacian operators. The problem is set in a bounded domain <semantics>D⊂RN</semantics> (<semantics>N≥3</semantics>) with homogeneous Dirichlet boundary conditions. A key feature of the system is the presence of a Hardy-type singular term with a variable exponent, where <semantics>δ(x)</semantics> represents the distance from x to the boundary <semantics>∂D</semantics>. By employing a critical point theorem in the framework of variable exponent Sobolev spaces, we establish the existence of a weak solution whose norm vanishes at zero.