The Existence of a Solution to a Class of Fractional Double Phase Problems

This paper focuses on the study of a class of fractional p&q-Laplacian problems with unbalanced growth, which includes vanishing potential and a supercritical growth exponent. By employing the mountain pass theorem alongside the Truncation method, penalization method, and Moser iteration method, the main result establishes the existence of a nontrivial solution under conditions of low perturbations of supercritical nonlinearity. Furthermore, we derive L∞(RN) estimates and the interior Hölder regularity of weak solutions in the context of supercritical growth.