SEMILINEAR NONLOCAL DIFFERENTIAL EQUATIONS WITH DELAY TERMS

Semilinear Nonlocal Differential Equations with Delay Terms

The goal of this paper is to obtain the regularity and the existence of solutions of a retarded semilinear differential equation with nonlocal condition by applying Schauder’s fixed point theorem. We construct the fundamental solution, establish the Hölder continuity results concerning the fundamental solution of its corresponding retarded linear equation, and prove the uniqueness of solutions ...

Semilinear Differential Equations with Nonlocal Conditions in Banach Spaces

In this paper we study the existence of mild solutions for the nonlocal Cauchy problem x′(t) = Ax(t) + f(t, x(t)), 0 < t ≤ b, x(0) = x0, by using the fixed point techniques, which extends and improves some existing results in this area.

Viability for Semilinear Differential Equations with Infinite Delay

Let X be a Banach space, A : D(A) ⊂ X → X the generator of a compact C0-semigroup S(t) : X → X, t ≥ 0, D(·) : (a, b)→ 2X a tube in X, and f : (a, b)×B → X a function of Carathéodory type. The main result of this paper is that a necessary and sufficient condition in order that D(·) be viable of the semilinear differential equation with infinite delay u′(t) = Au(t) + f (t, ut), t ∈ [t0, t0 + T], ...

Approximate Boundary Controllability for Semilinear Delay Differential Equations

Semilinear functional difference equations with infinite delay

We obtain boundness and asymptotic behavior of solutions for semilinear functional difference equations with infinite delay. Applications on Volterra difference equations with infinite delay are shown.