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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.
This paper studies a boundary value problem of nonlinear second-order q-difference equations with non-separated boundary conditions. As a first step, the given boundary value problem is converted to an equivalent integral operator equation by using the q-difference calculus. Then the existence and uniqueness of solutions of the problem is proved via the… (More)
This paper deals with the resolvent, asymptotic stability and boundedness of the solution of time-varying Volterra integro-dynamic system on time scales in which the coefficient matrix is not necessarily stable. We generalize to a time scale some known properties about asymptotic behavior and boundedness from the continuous case. Some new results for the… (More)
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.