Solvability of Nontrivial Solutions for a Discrete Fractional Boundary Value Problem

ABSTRACT In this work, we study a discrete fractional boundary value problem. By topological degree theory and some conditions involving the spectral radius of a positive linear operator, we obtain two existence theorems of nontrivial solutions when the nonlinearity can be sign‐changed. It is interesting that the boundary condition is very general being as it is allowed to be nonlocal and nonlinear, which can also be sign‐changing.