scholarly journals Existence results for some differential equations with deviating argument

Filomat ◽  
2011 ◽  
Vol 25 (2) ◽  
pp. 21-31 ◽  
Author(s):  
Monica Lauran
Keyword(s):  
Differential Equation ◽  
Banach Space ◽  
Differential Equations ◽  
Existence Of Solutions ◽  
Sufficient Conditions ◽  
Main Tool ◽  
Existence Results ◽  
Operator Technique ◽  
Nonexpansive Operator ◽  
Deviating Argument

In this paper we shall establish sufficient conditions for the existence of solutions of some differential equation and its solvability in CL, subset of the Banach space (C [a, b], ||?||). The main tool used in our study is the nonexpansive operator technique.

scholarly journals Lp-equivalence of a linear and a nonlinear impulsive differential equation in a Banach space

1993 ◽  
Vol 36 (1) ◽  
pp. 17-33 ◽  
Author(s):  
D. D. Bainov ◽  
S. I. Kostadinov ◽  
P. P. Zabreiko
Keyword(s):  
Differential Equation ◽  
Banach Space ◽  
Differential Equations ◽  
Impulsive Differential Equation ◽  
Sufficient Conditions ◽  
Impulsive Differential Equations

In the present paper by means of the Schauder-Tychonoff principle sufficient conditions are obtained for Lp-equivalence of a linear and a nonlinear impulsive differential equations.

scholarly journals Sufficient conditions for oscillations of all solutions of a class of impulsive differential equations with deviating argument

1996 ◽  
Vol 9 (1) ◽  
pp. 33-42 ◽  
Author(s):  
D. D. Bainov ◽  
M. B. Dimitrova
Keyword(s):  
Differential Equation ◽  
Differential Equations ◽  
Impulsive Differential Equation ◽  
Sufficient Conditions ◽  
Impulsive Differential Equations ◽  
Deviating Argument ◽  
All Solutions

Sufficient conditions are found for oscillation of all solutions of impulsive differential equation with deviating argument.

On Proper Oscillatory and Vanishing at Infinity Solutions of Differential Equations with A Deviating Argument

1995 ◽  
Vol 2 (4) ◽  
pp. 395-418
Author(s):  
I. Kiguradze ◽  
D. Chichua
Keyword(s):  
Differential Equation ◽  
Differential Equations ◽  
Sufficient Conditions ◽  
Integer Part ◽  
Deviating Argument ◽  
Measurable Functions ◽  
Carathéodory Conditions

Abstract Sufficient conditions are found for the existence of multiparametrical families of proper oscillatory and vanishing-at-infinity solutions of the differential equation u(n) (t) = g(t, u(τ 0 (t)); . . ., u(m–1) (τ m –1(t))), where n ≥ 4, m is the integer part of , g : R + × R m → R is a function satisfying the local Carathéodory conditions, and τi : R + → R (i = 0, . . . , m – 1) are measurable functions such that τ (t) → +∞ for t → + ∞ (i = 0, . . ., m – 1).

scholarly journals EXISTENCE RESULTS AND STABILITY CRITERIA FOR ABC-FUZZY-VOLTERRA INTEGRO-DIFFERENTIAL EQUATION

Fractals ◽  
2020 ◽  
Vol 28 (08) ◽  
pp. 2040048 ◽  
Author(s):  
HASIB KHAN ◽  
J. F. GOMEZ-AGUILAR ◽  
THABET ABDELJAWAD ◽  
AZIZ KHAN
Keyword(s):  
Differential Equation ◽  
Stability Analysis ◽  
Differential Equations ◽  
Numerical Simulations ◽  
Fractional Order ◽  
Existence Of Solutions ◽  
Existence Results ◽  
Ulam Stability ◽  
Stability Criteria ◽  
Science And Engineering

In the modeling of dynamical problems the fractional order integro-differential equations (IDEs) are very common in science and engineering. The scientists are developing different aspects of these models. The existence of solutions, stability analysis and numerical simulations are the most commonly studied aspects. There is no paper in literature describing the Hyers–Ulam stability (HU-stability) for fuzzy-fractional order models. Therefore, keeping the importance of the study, we consider the existence, uniqueness and HU-stability of a fractional order fuzzy-Volterra IDE.

Asymptotic behavior of evolution systems in arbitrary Banach spaces using general almost periodic splittings

2016 ◽  
Vol 8 (1) ◽  
pp. 1-28
Author(s):  
Josef Kreulich
Keyword(s):  
Differential Equation ◽  
Banach Space ◽  
Existence Of Solutions ◽  
Sufficient Conditions ◽  
Almost Periodicity ◽  
Almost Periodic ◽  
Initial Value ◽  
Dissipative Operators ◽  
Evolution Systems ◽  
General Banach Space

Abstract We present sufficient conditions on the existence of solutions, with various specific almost periodicity properties, in the context of nonlinear, generally multivalued, non-autonomous initial value differential equations, \frac{du}{dt}(t)\in A(t)u(t),\quad t\geq 0,\qquad u(0)=u_{0}, and their whole line analogues, {\frac{du}{dt}(t)\in A(t)u(t)} , {t\in\mathbb{R}} , with a family {\{A(t)\}_{t\in\mathbb{R}}} of ω-dissipative operators {A(t)\subset X\times X} in a general Banach space X. According to the classical DeLeeuw–Glicksberg theory, functions of various generalized almost periodic types uniquely decompose in a “dominating” and a “damping” part. The second main object of the study – in the above context – is to determine the corresponding “dominating” part {[A(\,\cdot\,)]_{a}(t)} of the operators {A(t)} , and the corresponding “dominating” differential equation, \frac{du}{dt}(t)\in[A(\,\cdot\,)]_{a}(t)u(t),\quad t\in\mathbb{R}.

scholarly journals Existence Results for a Coupled System of Nonlinear Fourth-Order Differential Equations

2013 ◽  
Vol 2013 ◽  
pp. 1-9 ◽  
Author(s):  
Bessem Samet
Keyword(s):  
Differential Equations ◽  
Fourth Order ◽  
Existence Of Solutions ◽  
Sufficient Conditions ◽  
Coupled System ◽  
Existence Results

Sufficient conditions are obtained for the existence of solutions to a coupled system of nonlinear fourth-order differential equations.

scholarly journals Optimal Controls for a Class of Impulsive Katugampola Fractional Differential Equations with Nonlocal Conditions

2020 ◽  
Vol 2020 ◽  
pp. 1-9
Author(s):  
Xingru Chen ◽  
Haibo Gu ◽  
Yu Sun
Keyword(s):  
Banach Space ◽  
Fixed Point ◽  
Differential Equations ◽  
Fractional Differential Equations ◽  
Nonlocal Conditions ◽  
Sufficient Conditions ◽  
Existence Results ◽  
Optimal Controls ◽  
Minimizing Sequences ◽  
Fractional Differential

In this paper, we investigate a class of impulsive Katugampola fractional differential equations with nonlocal conditions in a Banach space. First, by using a fixed-point theorem, we obtain the existence results for a class of impulsive Katugampola fractional differential equations. Secondly, we derive the sufficient conditions for optimal controls by building approximating minimizing sequences of functions twice.

Properties 𝐴 and 𝐵 of 𝑛th Order Linear Differential Equations with Deviating Argument

1999 ◽  
Vol 6 (6) ◽  
pp. 553-566
Author(s):  
R. Koplatadze ◽  
G. Kvinikadze ◽  
I. P. Stavroulakis
Keyword(s):  
Differential Equation ◽  
Differential Equations ◽  
Linear Differential Equation ◽  
Ordinary Differential Equations ◽  
Sufficient Conditions ◽  
Order Linear Differential Equation ◽  
Deviating Arguments ◽  
Order Linear ◽  
Deviating Argument ◽  
Linear Differential

Abstract Sufficient conditions for the nth order linear differential equation 𝑢(𝑛) (𝑡) + 𝑝(𝑡)𝑢(τ(𝑡)) = 0, 𝑛 ≥ 2, to have Property 𝐴 or Property 𝐵 are established in both the delayed and the advanced cases. These conditions essentially improve many known results not only for differential equations with deviating arguments but for ordinary differential equations as well.

scholarly journals Existence of solutions to Sobolev-type partial neutral differential equations

2006 ◽  
Vol 2006 ◽  
pp. 1-10 ◽  
Author(s):  
Shruti Agarwal ◽  
Dhirendra Bahuguna
Keyword(s):  
Differential Equation ◽  
Banach Space ◽  
Fixed Point ◽  
Fixed Point Theorem ◽  
Differential Equations ◽  
Point Theorem ◽  
Existence Of Solutions ◽  
Neutral Differential Equation ◽  
Sobolev Type ◽  
Neutral Differential Equations

This work is concerned with a nonlocal partial neutral differential equation of Sobolev type. Specifically, existence of the solutions to the abstract formulations of such type of problems in a Banach space is established. The results are obtained by using Schauder's fixed point theorem. Finally, an example is provided to illustrate the applications of the abstract results.

Initial Value Problem of Fractional Integro-Differential Equations in Banach Space

2015 ◽  
Vol 18 (1) ◽  
Author(s):  
Adel Jawahdou
Keyword(s):  
Differential Equation ◽  
Banach Space ◽  
Fixed Point ◽  
Fixed Point Theorem ◽  
Differential Equations ◽  
Point Theorem ◽  
Initial Value Problem ◽  
Measure Of Noncompactness ◽  
Existence Of Solutions ◽  
Initial Value

AbstractThis paper is devoted to study the existence of solutions of nonlinear fractional integro-differential equation, via the techniques of measure of noncompactness. The investigation is based on a Schauder's fixed point theorem. The main result is less restrictive than those given in the literature. An illustrative example is given.

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