Boundary value problems for functional difference equations on infinite intervals

Boundary Value Problems for Functional Difference Equations on Infinite Intervals

Some Boundary Value Problems on Infinite Intervals for Functional Differential Systems

< +∞. (3) Earlier, these problems were studied only in the cases, where f1 and f2 are either the Nemytski’s operators ([3], [4], [5]), or the linear operators ([1], [2], [6]). Below, we will present new, and in a certain sense, unimprovable conditions which guarantee, respectively, the solvability and well-posedness of (1), (2) and (1), (3). Throughout the paper, the following notation will be ...

Existence of Positive Solutions of Boundary Value Problems for Second-order Functional Differential Equations on Infinite Intervals

In present paper, the author investigates the existence of positive solutions of boundaryvalue problems for second-order functional differential equations on infinite intervals as followsx′′ − p(t)x′ − q(t)x+ f(t, xt,xt) = 0, t ∈ I = [0,∞),αx(t)− βx′(t) = ξ(t) ≥ 0, t ∈ [−τ, 0], ξ(0) = x(∞) = 0,where α ≥ 0, β > 0, ξ(t) ∈ C[−τ, 0]. By applying fixed point index theorem on cone...

On Nonlinear Boundary Value Problems for Functional Difference Equations with p-Laplacian

The existence of solutions of boundary value problems for finite difference equations were studied by many authors, one may see the text books 1, 2 , the papers 3–5 and the references therein. We present some representative ones, which are the motivations of this paper. In papers 3, 4 , using Krasnoselskii fixed point theorem and Leggett-Williams fixed point theorem, respectively, Karakostas st...

Periodic Boundary Value Problems for First Order Difference Equations

In this paper, existence criteria for single and multiple positive solutions of periodic boundary value problems for first order difference equations of the form