Study of Generalized Double Phase Problem with ς-Laplacian Operator

Abstract

In this paper, we explore a novel class of double-phase $$\varsigma $$ -Laplacian equation problems involving a $$\phi $$ -Hilfer fractional operator. Employing variational techniques and weighted Musielak space theory, we establish the existence of infinitely many positive solutions under suitable assumptions about the nonlinearity. Our main results are original and significantly advance the literature on problems featuring $$\phi $$ -Hilfer derivatives and the $$\varsigma $$ -Laplacian operator, thereby broadening the understanding of this particular class of problems.