scholarly journals Generalized Solutions of Functional Differential Inclusions

2008 ◽  
Vol 2008 ◽  
pp. 1-35 ◽  
Author(s):  
Anna Machina ◽  
Aleksander Bulgakov ◽  
Anna Grigorenko
Keyword(s):  
Asymptotic Properties ◽  
Local Existence ◽  
Approximate Solutions ◽  
Generalized Solution ◽  
Generalized Solutions ◽  
Initial Value ◽  
Absolutely Continuous ◽  
Functional Differential ◽  
Density Principle ◽  
Functional Differential Inclusions

We consider the initial value problem for a functional differential inclusion with a Volterra multivalued mapping that is not necessarily decomposable inL1n[a,b]. The concept of the decomposable hull of a set is introduced. Using this concept, we define a generalized solution of such a problem and study its properties. We have proven that standard results on local existence and continuation of a generalized solution remain true. The question on the estimation of a generalized solution with respect to a given absolutely continuous function is studied. The density principle is proven for the generalized solutions. Asymptotic properties of the set of generalized approximate solutions are studied.

scholarly journals Generalized quasilinearization method for nonlinear functional differential equations

2003 ◽  
Vol 16 (1) ◽  
pp. 33-43 ◽  
Author(s):  
Bashir Ahmad ◽  
Rehmat Ali Khan ◽  
S. Sivasundaram
Keyword(s):  
Differential Equations ◽  
Rate Of Convergence ◽  
Initial Value Problems ◽  
Functional Differential Equations ◽  
Approximate Solutions ◽  
Monotone Sequence ◽  
Quasilinearization Method ◽  
Initial Value ◽  
Nonlinear Functional ◽  
Functional Differential

We develop a generalized quasilinearization method for nonlinear initial value problems involving functional differential equations and obtain a sequence of approximate solutions converging monotonically and quadratically to the solution of the problem. In addition, we obtain a monotone sequence of approximate solutions converging uniformly to the solution of the problem, possessing the rate of convergence higher than quadratic.

scholarly journals A singular initial value problem for some functional differential equations

2004 ◽  
Vol 2004 (3) ◽  
pp. 261-270 ◽  
Author(s):  
Ravi P. Agarwal ◽  
Donal O'Regan ◽  
Oleksandr E. Zernov
Keyword(s):  
Differential Equations ◽  
Initial Value Problem ◽  
Asymptotic Properties ◽  
Functional Differential Equations ◽  
Initial Value ◽  
Singular Initial Value Problem ◽  
Functional Differential

For the initial value problem trx′(t)=at+b1x(t)+b2x(q1t)+b3trx′(q2t)+φ(t,x(t),x(q1t),x′(t),x′(q2t)), x(0)=0, where r>1, 0<qi≤1, i∈{1,2}, we find a nonempty set of continuously differentiable solutions x:(0,ρ]→ℝ, each of which possesses nice asymptotic properties when t→+0.

scholarly journals A study of a system of operator inclusions via a fixed point approach and applications to functional-differential inclusions

2016 ◽  
Vol 32 (3) ◽  
pp. 349-361 ◽  
Author(s):  
ADRIAN PETRUSEL ◽  
◽  
GABRIELA PETRUSEL ◽  
JEN-CHIH YAO ◽  
◽  
...  
Keyword(s):  
Fixed Point ◽  
Differential Inclusions ◽  
Metric Spaces ◽  
Mixed Boundary ◽  
Cartesian Product ◽  
Qualitative Properties ◽  
Initial Value ◽  
Functional Differential ◽  
The Given ◽  
Functional Differential Inclusions

In this paper, some existence results for a system of operator inclusions are presented. Qualitative properties of the solution set are also discussed. The method is based on the application of a fixed point theorem for an appropriate operator on the Cartesian product of the given spaces. The approach is new even for the case of the metric spaces. As an application, an existence result for a mixed boundary and initial value problem for a system of second order differential inclusions is given.

Generalized Solutions of Functional Differential Inclusions with a Volterra Multi-Valued Mapping

2007 ◽  
Author(s):  
Anna Machina ◽  
Aleksander Bulgakov ◽  
Theodore E. Simos ◽  
George Psihoyios ◽  
Ch. Tsitouras
Keyword(s):  
Differential Inclusions ◽  
Generalized Solutions ◽  
Functional Differential ◽  
Functional Differential Inclusions

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.

Impact of discontinuous harvesting policies on prey–predator system with Hassell–Varley-type functional response

2017 ◽  
Vol 10 (04) ◽  
pp. 1750048 ◽  
Author(s):  
Daozhong Luo ◽  
Dongshu Wang
Keyword(s):  
Functional Response ◽  
Local Existence ◽  
Degree Theory ◽  
Positive Periodic Solution ◽  
Predator Population ◽  
Topological Degree Theory ◽  
Functional Differential ◽  
Predator Model ◽  
Functional Differential Inclusions ◽  
Predator System

In this paper, a delayed prey–predator model with discontinuous harvesting policies is investigated, in which the predator population consumes the prey according to Hassell–Varley-type functional response. Under some reasonable assumptions on the discontinuous harvesting functions, the local existence and global existence of positive solution in sense of Filippov to the system are obtained. Based on the functional differential inclusions theory and the topological degree theory of set-valued analysis, a series of useful criteria on existence and non-existence of the positive periodic solution is established for the system. Finally, some numerical examples are given to show the applicability and effectiveness of the obtained results. It is worthy to point out that the discontinuous harvesting policies are superior to continuous harvesting policies, which are usually adopted in previous papers.

SOME PROPERTIES OF THE GENERALIZED SOLUTIONS OF AN INITIAL VALUE PROBLEM FOR FUNCTIONAL-DIFFERENTIAL INCLUSION WITH MULTIPLE-VALUED IMPULSES

2018 ◽  
pp. 805-812
Author(s):  
Olga Viktorovna Filippova ◽  
Andrey Igorevich Shindiapin
Keyword(s):  
Differential Inclusion ◽  
Initial Value Problem ◽  
Continuous Dependence ◽  
Continuous Functions ◽  
Generalized Solutions ◽  
Initial Value ◽  
Functional Differential Inclusion ◽  
Starting Conditions ◽  
Piecewise Continuous ◽  
Functional Differential

Deviation estimates in space of piecewise continuous functions of a set of the generalized decisions from beforehand given function are received. The continuous dependence of the generalized decisions on starting conditions is established.

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