Initial boundary value problems for second order impulsive functional differential inclusions

In this paper we investigate the existence of solutions for initial and boundary value problems for second order impulsive functional differential inclusions. We shall rely on a fixed point theorem for contraction multivalued maps due to Covitz and Nadler

Existence results for impulsive dynamic inclusions on time scales

In this paper, we investigate the existence of solutions and extremal solutions for a first order impulsive dynamic inclusion on time scales. By using suitable fixed point theorems, we study the case when the right hand side has convex as well as nonconvex values

Global attractivity of solutions for nonlinear fractional order Riemann-Liouville Volterra-Stieltjes partial integral equations

This paper deals with the existence and the attractivity of solutions of a class of fractional order functional Riemann-Liouville Volterra-Stieltjes partial integral equations. Our results are obtained by using Schauder's fixed point theorem

Existence results for first order impulsive semilinear evolution inclusions

In this paper the concepts of lower mild and upper mild solutions combined with a fixed point theorem for condensing maps and the semigroup theory are used to investigate the existence of mild solutions for first order impulsive semilinear evolution inclusions

Ulam Stability for Partial Fractional Differential Inclusions via Picard Operators Theory

In the present paper, we investigate, using the Picard operator technique, some existence and Ulam type stability results for the Darboux problem associated to some partial fractional order differential inclusions

Weak solutions for nonlinear fractional differential equations on reflexive Banach spaces

The aim of this paper is to investigate a class of boundary value problem for fractional differential equations involving nonlinear integral conditions. The main tool used in our considerations is the technique associated with measures of weak noncompactness

An existence result for first-order impulsive functional differential equations in banach spaces

AbstractIn this paper, the Leray-Schauder nonlinear alternative is used to investigate the existence of solutions to first-order impulsive initial value problems for functional differential equations in Banach spaces

Impulsive differential inclusions involving evolution operators in separable Banach spaces

We present some results on the existence of mild solutions and study the topological structures of the sets of solutions for the following first-order impulsive semilinear differential inclusions with initial and boundary conditions: where J=R+, 0 = t 0 < t 1 < … < t m <…, m∈N, lim k→∞ t k = ∞, A(t) is the infinitesimal generator of a family of evolution operators U(t, s) in a separable Banach space E and F is a set-valued mapping. The functions I k characterize the jumps of solutions at the impulse points t k , k = 1, ….The mapping L: PC b →E is a bounded linear operator. We also investigate the compactness of the set of solutions, some regularity properties of the operator solutions, and the absolute retract.Наведено деякi результати про iснування м’яких розв’язкiв та вивчено топологiчну будову множин розв’язкiв для наступних iмпульсних напiвлiнiйних диференцiальних включень першого порядку з початковими та граничними умовами: де J=IR+,0=t0<t1<...<tm<...;(m∈N),limk→∞tk=∞,A(t) — iнфiнiтезимальний генератор сiм’ї операторiв еволюцiї U(t,s) на сепарабельному банаховому просторi E та F — багатозначне вiдображення. Функцiї Ik характеризують стрибки розв’язкiв в точках iмпульсної дiї tk,k=1,... . Вiдображення L:PCb→E є обмеженим лiнiйним оператором. Також дослiджено компактнiсть множини розв’язкiв, деякi властивостi регулярностi операторних розв’язкiв та абсолютну ретрактнiсть

Boundary value problems for doubly perturbed first order ordinary differential systems

The aim of this paper is to present new results on existence theory for perturbed BVPs for first order ordinary differential systems. A nonlinear alternative for the sum of a contraction and a compact mapping is used

Functional differential inclusions with integral boundary conditions

In this paper, we investigate the existence of solutions for a class of second order functional differential inclusions with integral boundary conditions. By using suitable fixed point theorems, we study the case when the right hand side has convex as well as nonconvex values