STUDY OF SCHRÖDINGER-CHOQUARD PROBLEM WITH <i>P</i>(·)-LAPLACIAN OPERATOR

In this paper, our focus is on a specific class of non-linear $ \psi $-Hilfer fractional generalized Schrödinger-Choquard differential equations involving the $ p(\cdot) $-Laplacian operator with Dirichlet boundary conditions. By employing the mountain pass theorem without the Palais–Smale condition, along with the Hardy-Littlewood-Sobolev inequality with variable exponents, we establish the existence of a weak solution to our problem. Our main results are novel and contribute to the literature on problems involving $ \psi $-Hilfer derivatives with the $ p(\cdot) $-Laplacian operator. This investigation enhances the scope of understanding in this specific class of problems.