Existence of weak solutions for fractional (p_1(x,y),p_2(x,y))-Laplacian problems with indefinite weights

Abstract

We study nonlocal elliptic problems driven by the fractional \((p_1(x,y),p_2(x,y))\)-Laplacian operator under Dirichlet boundary conditions, where \(p_1(\cdot,\cdot)\) and \(p_2(\cdot,\cdot)\) are continuous functions defined on a bounded domain \(\Omega\subset\mathbb{R}^N\) (\(N\geq 2\)). The model includes indefinite weight functions, which may change the sign within the domain. By applying variational methods, we establish the existence of at least one nontrivial weak solution. Our results extend recent contributions in the literature on nonlocal problems with variable exponent operators, and provide new insights into the interaction between fractional order, and sign-changing weights. For more information and the latex file, see https://ejde.math.txstate.edu/Volumes/2026/40/abstr.html