Solvability of Boundary Value Problems for a Class of Third-Order Functional Difference Equations

Consider the boundary value problems consisting of the functional difference equationΔ³x(n)=f(n,x(n+2),x(n-τ₁(n)),,x(n-τₘ(n))),\;\;n∈[0,T] and the following boundary value conditions\[{cases}x(0)=x(T+3)=x(1)=0,\(n)=ψ(n), \;n∈ [-τ,-1],\(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