Nontrivial solutions for a nonlinear νth order Atıcı-Eloe fractional difference equation satisfying Dirichlet boundary conditions

Abstract

. For 1 < ν (cid:2) 2 a real number and T (cid:3) 2 a natural number, by an application of a Krasnosel’skii-Zabreiko fi xed point theorem, nontrivial solutions are established for a nonlinear ν th order At ı c ı -Eloe fractional difference equation, Δ ν u ( t )+ f ( u ( t + ν − 1 )) = 0, t ∈ { 1 , 2 ,..., T + 1 } , satisfying the Dirichlet boundary conditions u ( ν − 2 ) = u ( ν + T + 1 ) = 0 ,