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Displaying 161 – 180 of 199

Retarded functional differential equations in Banach spaces and Henstock-Kurzweil-Pettis integrals

A. Sikorska-Nowak (2007)

Discussiones Mathematicae, Differential Inclusions, Control and Optimization

We prove an existence theorem for the equation x' = f(t,xₜ), x(Θ) = φ(Θ), where xₜ(Θ) = x(t+Θ), for -r ≤ Θ < 0, t ∈ Iₐ, Iₐ = [0,a], a ∈ R₊ in a Banach space, using the Henstock-Kurzweil-Pettis integral and its properties. The requirements on the function f are not too restrictive: scalar measurability and weak sequential continuity with respect to the second variable. Moreover, we suppose that the function f satisfies some conditions expressed in terms of the measure of weak noncompactness.

Robustness with respect to small time-varied delay for linear dynamical systems on Banach spaces

Miao Li, Xiao-Hui Gu, Fa-Lun Huang (2004)

Studia Mathematica

Under suitable conditions we prove the wellposedness of small time-varied delay equations and then establish the robust stability for such systems on the phase space of continuous vector-valued functions.

Second order evolution equations with parameter

Jan Bochenek, Teresa Winiarska (1994)

Annales Polonici Mathematici

We give some theorems on continuity and differentiability with respect to (h,t) of the solution of a second order evolution problem with parameter $h \in Ω \subset ℝ^{m}$ . Our main tool is the theory of strongly continuous cosine families of linear operators in Banach spaces.

Semigroup approach to semilinear partial functional differential equations with infinite delay.

Bouzahir, Hassane (2007)

Journal of Inequalities and Applications [electronic only]

Semilinear fractional order integro-differential equations with infinite delay in Banach spaces

Khalida Aissani, Mouffak Benchohra (2013)

Archivum Mathematicum

This paper concerns the existence of mild solutions for fractional order integro-differential equations with infinite delay. Our analysis is based on the technique of Kuratowski’s measure of noncompactness and Mönch’s fixed point theorem. An example to illustrate the applications of main results is given.

Semilinear functional differential equations of fractional order with state-dependent delay.

Darwish, Mohamed Abdalla, Ntouyas, Sotiris K. (2009)

Electronic Journal of Differential Equations (EJDE) [electronic only]

Solution semigroup and invariant manifolds for functional equations with infinite delay

Hana Petzeltová (1993)

Mathematica Bohemica

It is proved that parabolic equations with infinite delay generate $C_{0}$ -semigroup on the space of initial conditions, such that local stable and unstable manifolds can be constructed for a fully nonlinear problems with help of usual methods of the theory of parabolic equations.

Spectral properties and finite pole assignment of linear neutral systems in Banach spaces.

Xia, Xuewen, Liu, Kai (2010)

Abstract and Applied Analysis

Stability and saddle-point property for a linear autonomous functional parabolic equation

Jaroslav Milota (1986)

Commentationes Mathematicae Universitatis Carolinae

Stability and stabilizability of mixed retarded-neutral type systems

Rabah Rabah, Grigory Mikhailovitch Sklyar, Pavel Yurevitch Barkhayev (2012)

ESAIM: Control, Optimisation and Calculus of Variations

We analyze the stability and stabilizability properties of mixed retarded-neutral type systems when the neutral term may be singular. We consider an operator differential equation model of the system in a Hilbert space, and we are interested in the critical case when there is a sequence of eigenvalues with real parts converging to zero. In this case, the system cannot be exponentially stable, and we study conditions under which it will be strongly stable. The behavior of spectra of mixed retarded-neutral...

Stability and stabilizability of mixed retarded-neutral type systems∗

Rabah Rabah, Grigory Mikhailovitch Sklyar, Pavel Yurevitch Barkhayev (2012)

ESAIM: Control, Optimisation and Calculus of Variations

Stability and stabilizability of mixed retarded-neutral type systems∗

Rabah Rabah, Grigory Mikhailovitch Sklyar, Pavel Yurevitch Barkhayev (2012)

ESAIM: Control, Optimisation and Calculus of Variations

Stability of solutions for nonlinear nonautonomous differential-delay equations in Hilbert spaces.

Gil', Michael I. (2002)

Electronic Journal of Differential Equations (EJDE) [electronic only]

Stepanov-like square-mean pseudo almost automorphic solutions to partial neutral stochastic functional differential equations

Zuomao Yan, Xiu-Mei Jia, Xingxue Yan (2013)

Annales Polonici Mathematici

We obtain the existence and uniqueness of square-mean pseudo almost automorphic mild solutions to first-order partial neutral stochastic functional differential equations with Stepanov-like almost automorphic coefficients in a real separable Hilbert space.

Stochastic differential equations in Hilbert spaces

Anna Chojnowska-Michalik (1979)

Banach Center Publications

Stochastic stability of Cohen-Grossberg neural networks with unbounded distributed delays.

Chen, Ping, Huang, Chuangxia, Liang, Xiaolin (2010)

Electronic Journal of Differential Equations (EJDE) [electronic only]

Strong solutions for some nonlinear partial functional differential equations with infinite delay.

Alia, Mohamed, Ezzinbi, Khalil (2008)

Electronic Journal of Differential Equations (EJDE) [electronic only]

Study of a complete abstract differential equation of elliptic type with variable operator coefficients, I.

Angelo Favini, Rabah Labbas, Keddour Lemrabet, Boubaker-Khaled Sadallah (2008)

Revista Matemática Complutense

Study of Stability in Nonlinear Neutral Differential Equations with Variable Delay Using Krasnoselskii–Burton’s Fixed Point

Mouataz Billah MESMOULI, Abdelouaheb Ardjouni, Ahcene Djoudi (2016)

Acta Universitatis Palackianae Olomucensis. Facultas Rerum Naturalium. Mathematica

In this paper, we use a modification of Krasnoselskii’s fixed point theorem introduced by Burton (see [Burton, T. A.: Liapunov functionals, fixed points and stability by Krasnoseskii’s theorem. Nonlinear Stud., 9 (2002), 181–190.] Theorem 3) to obtain stability results of the zero solution of the totally nonlinear neutral differential equation with variable delay $x^{'} (t) = - a (t) h (x (t)) + \frac{d}{d t} Q (t, x (t - τ (t))) + G (t, x (t), x (t - τ (t))) .$ The stability of the zero solution of this eqution provided that $h (0) = Q (t, 0) = G (t, 0, 0) = 0$ . The Caratheodory condition is used for the functions $Q$ and $G$ .

Study of the limit of transmission problems in a thin layer by the sum theory of linear operators.

Angelo Favini, Rabah Labbas, Keddour Lemrabet, Stéphane Maingot (2005)

Revista Matemática Complutense

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