Solvability of Boundary Value Problems for a Class of Third-Order Functional Difference Equations - Liu, Yuji (Sarajevo Journal of Mathematics, 2024)
Consider the boundary value problems consisting of the functional difference equation Δ^3x(n)=f(n,x(n+2),x(n-τ_1(n)),…,x(n-τ_m(n))), n [0,T] and the following boundary value conditions \[cases x(0)=x(T+3)=x(1)=0, x(n)=ψ(n), n[-τ,-1], x(n)=φ(n), n[T+4,T+δ].cases \] Sufficient conditions for the existence of at least one solution of this problem are established. We allow f to be at most linear, superlinear or sublinear in the obtained results. 2000 Mathematics Subject Classification. 34B10, 34B15, 39A10