Dedication We dedicate this book to our family members who complete us. In particular, M. Ben-chohra's dedication is to his wife, Kheira, and his children, Mohamed, Maroua, and Abdelillah; J. Henderson dedicates to his wife, Darlene, and his descendants, Kathy, Contents Preface xi 1. Preliminaries 1 1.1. Definitions and results for multivalued analysis 1… (More)
In this paper, we first present an impulsive version of Filippov's Theorem for first-order neutral functional differential inclusions of the form, d dt [y(t) − g(t, yt)] ∈ F (t, yt), y(t + k) − y(t − k) = I k (y(t − k)), k = 1,. .. , m, y(t) = φ(t), t ∈ [−r, 0], where J = [0, b], F is a set-valued map and g is a single-valued function. The functions I k… (More)
In this paper, we shall establish sufficient conditions for the existence of solutions for a first order boundary value problem for fractional differential equations. References  L. Byszewski, Theorems about existence and uniqueness of solutions of a semi-linear evolution nonlocal Cauchy problem,  L. Byszewski, Existence and uniqueness of mild and… (More)
In this paper, we study the existence of solutions for a boundary value problem of differential inclusions of order q ∈ (1, 2] with non-separated boundary conditions involving convex and non-convex multivalued maps. Our results are based on the nonlinear alternative of Leray Schauder type and some suitable theorems of fixed point theory.
The Banach fixed point theorem and the nonlinear alternative of Leray–Schauder type are used to investigate the existence of solutions for fractional order functional and neutral functional differential equations with infinite delay.
Values of λ are determined for which there exist positive solutions of the system of three-point boundary value problems, u ′′ + λa(t)f (v) = 0, v ′′ + λb(t)g(u) = 0, for 0 < t < 1, and satisfying, u(0) = βu(η), u(1) = αu(η), v(0) = βv(η), v(1) = αv(η). A Guo-Krasnosel'skii fixed point theorem is applied.
Intervals of the parameter λ are determined for which there exist positive solutions for the system of nonlinear differential equations, u (n) + λa(t)f (v) = 0, v (n) + λb(t)g(u) = 0, for 0 < t < 1, and satisfying three-point nonlocal bound-(0) = 0, v(1) = αv(η). A Guo-Krasnosel'skii fixed point theorem is applied.
In this paper we prove controllability results for mild solutions defined on a compact real interval for first order differential evolution inclusions in Banach spaces with non-local conditions. By using suitable fixed point theorems we study the case when the multi-valued map has convex as well as non-convex values.