Multiple Solutions to the Fractional p-Laplacian Equations of Schrödinger-Hardy-Type Involving Concave-Convex Nonlinearities

This paper is concerned with nonlocal fractional p-Laplacian Schr & ouml;dinger-Hardy-type equations involving concave-convex nonlinearities. The first aim is to demonstrate the L-infinity-bound for any possible weak solution to our problem. As far as we know, the global a priori bound for weak solutions to nonlinear elliptic problems involving a singular nonlinear term such as Hardy potentials has not been studied extensively. To overcome this, we utilize a truncated energy technique and the De Giorgi iteration method. As its application, we demonstrate that the problem above has at least two distinct nontrivial solutions by exploiting a variant of Ekeland's variational principle and the classical mountain pass theorem as the key tools. Furthermore, we prove the existence of a sequence of infinitely many weak solutions that converges to zero in the L-infinity-norm. To derive this result, we employ the modified functional method and the dual fountain theorem.