On the functional boundary value problems involving a fractional p −Laplacian operator with a two-dimensional kernel

Abstract

We obtain, by generalizing the extension of the continuous theorem of Ge and Ren and constructing suitable Banach spaces and operators, two results about the existence of solutions for fractional differential equations with resonant p-Laplacian and functional boundary conditons. Meanwhile, the dimension of the kernel for a fractional differential operator with boundary conditions is two, which generalises and enrichs some known results. An novel example is also given to illustrate the existence theorem. Mathematics Subject Classification. Primary 34A08; Secondary 34B15