scholarly journals Existence results for second order functional differential and integrodifferential inclusions in Banach spaces

2001 ◽  
Vol 32 (4) ◽  
pp. 315-325
Author(s):  
M. Benchohra ◽  
S. K. Ntouyas
Keyword(s):  
Fixed Point ◽  
Fixed Point Theorem ◽  
Banach Spaces ◽  
Initial Value Problems ◽  
Existence Of Solutions ◽  
Existence Results ◽  
Second Order ◽  
Initial Value ◽  
Functional Differential ◽  
Condensing Maps

In this paper we investigate the existence of solutions on a compact interval to second order initial value problems for functional differential and integrodifferential inclusions in Banach spaces. We shall make use of a fixed point theorem for condensing maps due to Martelli.

scholarly journals On second-order multivalued impulsive functional differential inclusions in Banach spaces

2001 ◽  
Vol 6 (6) ◽  
pp. 369-380 ◽  
Author(s):  
M. Benchohra ◽  
J. Henderson ◽  
S. K. Ntouyas
Keyword(s):  
Fixed Point ◽  
Fixed Point Theorem ◽  
Banach Spaces ◽  
Differential Inclusions ◽  
Existence Of Solutions ◽  
Second Order ◽  
Initial Value ◽  
Functional Differential ◽  
Functional Differential Inclusions ◽  
Condensing Maps

A fixed point theorem for condensing maps due to Martelli is used to investigate the existence of solutions to second-order impulsive initial value problem for functional differential inclusions in Banach spaces.

scholarly journals Existence results for second-order impulsive functional differential inclusions

2006 ◽  
Vol 2006 ◽  
pp. 1-12 ◽  
Author(s):  
Yong-Kui Chang ◽  
Li-Mei Qi
Keyword(s):  
Fixed Point ◽  
Fixed Point Theorem ◽  
Point Theorem ◽  
Differential Inclusions ◽  
Existence Of Solutions ◽  
Existence Results ◽  
Second Order ◽  
Compact Interval ◽  
Functional Differential ◽  
Functional Differential Inclusions

The existence of solutions on a compact interval to second-order impulsive functional differential inclusions is investigated. Several new results are obtained by using Sadovskii's fixed point theorem.

scholarly journals On second order impulsive functional differential equations in Banach spaces

2002 ◽  
Vol 15 (1) ◽  
pp. 45-52 ◽  
Author(s):  
M. Benchohra ◽  
S. K. Ntouyas
Keyword(s):  
Fixed Point ◽  
Fixed Point Theorem ◽  
Differential Equations ◽  
Banach Spaces ◽  
Point Theorem ◽  
Existence Of Solutions ◽  
Functional Differential Equations ◽  
Second Order ◽  
Functional Differential

In this paper, a fixed point theorem due to Schaefer is used to investigate the existence of solutions for second order impulsive functional differential equations in Banach spaces.

scholarly journals GLOBAL EXISTENCE RESULTS FOR FUNCTIONAL DIFFERENTIAL INCLUSIONS WITH STATE-DEPENDENT DELAY

2014 ◽  
Vol 19 (4) ◽  
pp. 524-536 ◽  
Author(s):  
Mouffak Benchohra ◽  
Johnny Henderson ◽  
Imene Medjadj
Keyword(s):  
Fixed Point ◽  
Fixed Point Theorem ◽  
Global Existence ◽  
Differential Inclusions ◽  
Existence Of Solutions ◽  
Existence Results ◽  
State Dependent ◽  
State Dependent Delay ◽  
Functional Differential ◽  
Functional Differential Inclusions

Our aim in this work is to study the existence of solutions of a functional differential inclusion with state-dependent delay. We use the Bohnenblust–Karlin fixed point theorem for the existence of solutions.

Solvability of initial value problems with fractional order differential equations in banach spaces by α-dense curves

2017 ◽  
Vol 20 (3) ◽  
Author(s):  
Gonzalo García
Keyword(s):  
Differential Equation ◽  
Banach Space ◽  
Fixed Point ◽  
Fixed Point Theorem ◽  
Initial Value Problems ◽  
Existence Of Solutions ◽  
Initial Value ◽  
Measures Of Noncompactness ◽  
Fractional Order Differential Equations ◽  
Fractional Differential

AbstractIn this paper we study the existence of solutions for an initial value problem, posed in a given Banach space, with a fractional differential equation via densifiability techniques. For our goal, we will prove a new fixed point result (not based on measures of noncompactness) which is, in forms, a generalization of the well-known Darbo’s fixed point theorem but essentially different. Some illustrative examples are given.

Existence Results on Infinite Intervals for Neutral Functional Differential and Integrodifferential Inclusions in Banach Spaces

2000 ◽  
Vol 7 (4) ◽  
pp. 609-625 ◽  
Author(s):  
M. Benchohra ◽  
S. K. Ntouyas
Keyword(s):  
Banach Spaces ◽  
Initial Value Problems ◽  
Mild Solutions ◽  
Existence Results ◽  
Topological Spaces ◽  
Initial Value ◽  
Infinite Intervals ◽  
Functional Differential ◽  
The Fixed Point Theorem ◽  
Locally Convex

Abstract In this paper we investigate the existence of mild solutions, on infinite intervals, to initial value problems for neutral functional differential and integrodifferential inclusions in Banach spaces. We shall rely on the fixed point theorem due to Ma, which is an extension on locally convex topological spaces, of Schaefer's theorem.

scholarly journals Existence of Solutions of a Class of Abstract Second Order Nonlinear Integrodifferential Equations

2002 ◽  
Vol 15 (2) ◽  
pp. 115-124 ◽  
Author(s):  
K. Balachandran ◽  
J. Y. Park
Keyword(s):  
Fixed Point ◽  
Fixed Point Theorem ◽  
Banach Spaces ◽  
Point Theorem ◽  
Existence Of Solutions ◽  
Second Order ◽  
Integrodifferential Equations ◽  
Cosine Families ◽  
Schaefer Fixed Point Theorem ◽  
Families Of Operators

In this paper we prove the existence of solutions of nonlinear second order integrodifferential equations in Banach spaces. The results are obtained by using the theory of strongly continuous cosine families of operators and the Schaefer fixed point theorem.

Controllability of Sobolev Type Semilinear Functional Differential and Integrodifferential Inclusions with an Unbounded Delay

2006 ◽  
Vol 13 (1) ◽  
pp. 11-24 ◽  
Author(s):  
Yong-Kui Chang ◽  
Wan-Tong Li
Keyword(s):  
Fixed Point ◽  
Fixed Point Theorem ◽  
Banach Spaces ◽  
Point Theorem ◽  
Sufficient Conditions ◽  
Sobolev Type ◽  
Unbounded Delay ◽  
Functional Differential ◽  
The Fixed Point Theorem ◽  
Condensing Maps

Abstract In this paper, sufficient conditions are established for the controllability of Sobolev type semilinear functional differential and integrodifferential inclusions with an unbounded delay in Banach spaces. The main results are obtained by using the fixed point theorem for condensing maps due to Martelli.

scholarly journals A method of upper and lower solutions for functional differential inclusions

2002 ◽  
Vol 15 (3) ◽  
pp. 269-276
Author(s):  
Mouffak Benchohra ◽  
Sotiris K. Ntouyas
Keyword(s):  
Fixed Point ◽  
Fixed Point Theorem ◽  
Point Theorem ◽  
Differential Inclusions ◽  
Existence Of Solutions ◽  
Upper And Lower Solutions ◽  
First Order ◽  
Functional Differential ◽  
Functional Differential Inclusions ◽  
Condensing Maps

In this paper, a fixed point theorem for condensing maps combined with upper and lower solutions are used to investigate the existence of solutions for first order functional differential inclusions.

scholarly journals On the existence of solutions for Volterra integral inclusions in Banach spaces

1993 ◽  
Vol 6 (3) ◽  
pp. 261-269
Author(s):  
Evgenios P. Avgerinos
Keyword(s):  
Banach Space ◽  
Fixed Point ◽  
Fixed Point Theorem ◽  
Existence Of Solutions ◽  
Existence Results ◽  
The Other ◽  
Multivalued Map ◽  
Volterra Type ◽  
The Right ◽  
Condensing Maps

In this paper we examine a class of nonlinear integral inclusions defined in a separable Banach space. For this class of inclusions of Volterra type we establish two existence results, one for inclusions with a convex-valued orientor field and the other for inclusions with nonconvex-valued orientor field. We present conditions guaranteeing that the multivalued map that represents the right-hand side of the inclusion is α-condensing using for the proof of our results a known fixed point theorem for α-condensing maps.

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