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 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 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 Multivalued impulsive neutral functional differential inclusions in Banach spaces

2002 ◽  
Vol 33 (1) ◽  
pp. 67-78
Author(s):  
M. Benchohra ◽  
J. Henderson ◽  
S. K. Ntouyas
Keyword(s):  
Fixed Point ◽  
Fixed Point Theorem ◽  
Banach Spaces ◽  
Point Theorem ◽  
Differential Inclusions ◽  
Existence Of Solutions ◽  
Semigroup Theory ◽  
Multivalued Maps ◽  
Functional Differential ◽  
Functional Differential Inclusions

In paper the existence of solutions for first and second order impulsive neutral functional differential inclusions in Banach spaces is investigated. The results are obtained by using a fixed point theorem for condensing multivalued maps due to Martelli and the semigroup theory.

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.

scholarly journals Upper and Lower Solutions form-Point Impulsive BVP with One-Dimensionalp-Laplacian

2013 ◽  
Vol 2013 ◽  
pp. 1-9 ◽  
Author(s):  
Junfang Zhao ◽  
Jianfeng Zhao ◽  
Weigao Ge
Keyword(s):  
Fixed Point ◽  
Fixed Point Theorem ◽  
Boundary Value Problems ◽  
Positive Solutions ◽  
Point Theorem ◽  
Nonlinear Term ◽  
Existence Of Solutions ◽  
Upper And Lower Solutions ◽  
First Order ◽  
Impulsive Boundary Value Problems

Upper and lower solutions theories are established for a kind ofm-point impulsive boundary value problems withp-Laplacian. By using such techniques and the Schauder fixed point theorem, the existence of solutions and positive solutions is obtained. Nagumo conditions play an important role in the nonlinear term involved with the first-order derivatives.

scholarly journals Controllability of Impulsive Neutral Functional Differential Inclusions in Banach Spaces

2013 ◽  
Vol 2013 ◽  
pp. 1-8 ◽  
Author(s):  
X. J. Wan ◽  
Y. P. Zhang ◽  
J. T. Sun
Keyword(s):  
Fixed Point ◽  
Fixed Point Theorem ◽  
Banach Spaces ◽  
Point Theorem ◽  
Differential Inclusions ◽  
Sufficient Conditions ◽  
Controllability Problem ◽  
Special Cases ◽  
Functional Differential ◽  
Functional Differential Inclusions

We investigate the controllability of impulsive neutral functional differential inclusions in Banach spaces. Our main aim is to find an effective method to solve the controllability problem of impulsive neutral functional differential inclusions with multivalued jump sizes in Banach spaces. Based on a fixed point theorem with regard to condensing map, sufficient conditions for the controllability of the impulsive neutral functional differential inclusions in Banach spaces are derived. Moreover, a remark is given to explain less conservative criteria for special cases, and work is improved in the previous literature.

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 Neutral Functional Differential Inclusions involving Hadamard Fractional Derivatives

Mathematics ◽  
2019 ◽  
Vol 7 (11) ◽  
pp. 1084 ◽  
Author(s):  
Bashir Ahmad ◽  
Ahmed Alsaedi ◽  
Sotiris K. Ntouyas ◽  
Hamed H. Al-Sulami
Keyword(s):  
Fixed Point ◽  
Differential Inclusions ◽  
Fractional Derivatives ◽  
Fixed Point Theorems ◽  
Existence Of Solutions ◽  
Multivalued Maps ◽  
Functional Differential ◽  
Functional Differential Inclusions

We prove the existence of solutions for neutral functional differential inclusions involving Hadamard fractional derivatives by applying several fixed point theorems for multivalued maps. We also construct examples for illustrating the obtained results.

scholarly journals Multivalued semilinear neutral functional differential equations with nonconvex-valued right-hand side

2004 ◽  
Vol 2004 (6) ◽  
pp. 525-541
Author(s):  
M. Benchohra ◽  
E. Gatsori ◽  
S. K. Ntouyas
Keyword(s):  
Fixed Point ◽  
Fixed Point Theorem ◽  
Point Theorem ◽  
Mild Solutions ◽  
Lower Semicontinuous ◽  
Functional Differential Equations ◽  
Neutral Functional Differential Equations ◽  
Multivalued Operators ◽  
Functional Differential ◽  
Functional Differential Inclusions

We investigate the existence of mild solutions on acompact interval to some classes of semilinear neutral functional differential inclusions. We will rely on a fixed-point theorem for contraction multivalued maps due to Covitz and Nadler and on Schaefer's fixed-point theorem combined with lower semicontinuous multivalued operators with decomposable values.

scholarly journals Existence results for fractional differential inclusions with Erdélyi-Kober fractional integral conditions

2017 ◽  
Vol 25 (2) ◽  
pp. 5-24 ◽  
Author(s):  
Bashir Ahmad ◽  
Sotiris K. Ntouyas
Keyword(s):  
Fixed Point ◽  
Fixed Point Theorem ◽  
Point Theorem ◽  
Differential Inclusions ◽  
Fractional Integral ◽  
Existence Of Solutions ◽  
Existence Results ◽  
Fractional Differential Inclusions ◽  
Integral Conditions ◽  
Fractional Differential

Abstract In this paper, we discus the existence of solutions for Riemann- Liouville fractional differential inclusions supplemented with Erdélyi- Kober fractional integral conditions. We apply endpoint theory, Krasnoselskii’s multi-valued fixed point theorem and Wegrzyk's fixed point theorem for generalized contractions. For the illustration of our results, we include examples.

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