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First order difference equations with maxima and nonlinear functional boundary value conditions. (English) Zbl 1107.39001

This paper is concerned with the existence of solutions of a difference equation of the form

Δu k =fk,u k+1 ,max k-h-1ik+1 u i ,k=0,1,2,,T-1,

that satisfies the additional conditions

u k =ϕ(k,u -h+1 ,,u T ),
Bu 0 ,u -h+1 ,,u T =0,

where h,T are positive integers, and ϕ and B are continuous functions. Monotone methods (using upper and lower solutions) together with monotone type assumptions are applied to obtain existence criteria. The two conditions above include, among others, initial, periodic, antiperiodic, and multipoint conditions.

39A10Additive difference equations
39A12Discrete version of topics in analysis