Multiplicity Result of Solutions to the Fractional Problems with (p,q)-Growth and Hardy Potentials

This paper focuses on establishing the existence of infinitely many solutions for non-local fractional equations characterized by unbalanced growth and Hardy potentials. We prove that these solutions converge to zero in the L∞-norm, requiring conditions on the nonlinearity only near the origin and dispensing with assumptions at infinity. As far as we are aware, results for non-local fractional (p,q)-Laplacian problems with singular coefficients such as Hardy potentials have not been extensively studied. To address this gap, we employ the dual fountain theorem together with the modified functional method.