TITLE

Mild solutions for impulsive semilinear evolution differential inclusions

AUTHOR(S)
Cardinali, Tiziana; Rubbioni, Paola
PUB. DATE
January 2006
SOURCE
Journal of Applied Functional Analysis;Jan2006, Vol. 1 Issue 1, p304
SOURCE TYPE
Academic Journal
DOC. TYPE
Abstract
ABSTRACT
In this paper we prove a sufficient condition for the existence of mild solutions for an impulsive Cauchy problem monitored by the semilinear evolution differential inclusion x′(t) ∈ A(t)x(t) + F(t, x(t)) where {A(t)}t ∈[0,b] is a family of linear operators in a Banach space E generating an evolution operator and F is a Carathèodory type multifunction. Since we do not assume any hypothesis on the impulse functions, our existence theorem extends in a broad sense a proposition obtained by Benchohra, Henderson and Ntouyas.
ACCESSION #
21352166

 

Related Articles

  • EXISTENCE OF SOLUTIONS FOR DIFFERENTIAL INCLUSIONS ON CLOSED MOVING CONSTRAINTS IN BANACH SPACES. GOMAA, ADEL MAHMOUD // Electronic Journal of Differential Equations;2009, Vol. 2009, Special section p1 

    In this paper, we prove the existence of solutions to a multivalued differential equation with moving constraints. We use a weak compactness type condition expressed in terms of a strong measure of noncompactness.

  • EXISTENCE OF SOLUTIONS FOR AN ABSTRACT SECOND-ORDER DIFFERENTIAL EQUATION WITH NONLOCAL CONDITIONS. HERNÁNDEZ, EDUARDO // Electronic Journal of Differential Equations;2009, Vol. 2009, Special section p1 

    We discuss the existence of mild solutions for abstract second-order differential equation with nonlocal conditions. Also we consider some application of our results.

  • Existence of the mild solution for some fractional differential equations with nonlocal conditions. Mophou, G.; N’Guérékata, G. // Semigroup Forum;Sep/Oct2009, Vol. 79 Issue 2, p315 

    We are concerned in this paper with the existence of mild solutions to the Cauchy Problem for the fractional differential equation with nonlocal conditions: D q x( t)= Ax( t)+ t n f( t, x( t), Bx( t)), t∈[0, T], n∈ℤ+, x(0)+ g( x)= x0, where 0< q<1, A is the infinitesimal...

  • EXISTENCE OF MILD SOLUTIONS OF A SEMILINEAR EVOLUTION DIFFERENTIAL INCLUSIONS WITH NONLOCAL CONDITIONS. AL-OMAIR, REEM A.; IBRAHIM, AHMED G. // Electronic Journal of Differential Equations;2009, Vol. 2009, Special section p1 

    In this paper we prove the existence of a mild solution for a semi-linear evolution differential inclusion with nonlocal condition and governed by a family of linear operators, not necessarily bounded or closed, in a Banach space. No compactness assumption is assumed on the evolution operator...

  • AN ABSTRACT CAUCHY PROBLEM FOR HIGHER ORDER FUNCTIONAL DIFFERENTIAL INCLUSIONS WITH INFINITE DELAY. Tran Dinh Ke; Obukhovskii, Valeri; Ngai-Ching Wong; Jen-Chih Yao // Discussiones Mathematicae: Differential Inclusions, Control & Op;2011, Vol. 31 Issue 2, p199 

    The existence results for an abstract Cauchy problem involving a higher order differential inclusion with infinite delay in a Banach space are obtained. We use the concept of the existence family to express the mild solutions and impose the suitable conditions on the nonlinearity via the measure...

  • CLASSES OF MEROMORPHIC FUNCTIONS DEFINED BY THE EXTENDED SÄ‚LÄ‚GEAN OPERATOR. Dziok, Jacek // Studia Universitatis Babes-Bolyai, Mathematica;2010, Issue 3, p123 

    In the paper, we define classes of meromorphic functions, in terms of the extended Sălăgean operator. By using Jack's Lemma and the Briot-Bouquet differential subordination we obtain some inclusion relations for defined classes.

  • Partial asymptotic stability of abstract differential equations. Zuev, A. L. // Ukrainian Mathematical Journal;May2006, Vol. 58 Issue 5, p709 

    We consider the problem of partial asymptotic stability with respect to a continuous functional for a class of abstract dynamical processes with multivalued solutions on a metric space. This class of processes includes finite-and infinite-dimensional dynamical systems, differential inclusions,...

  • Applications of the theory of degenerate operator semigroups to initial-boundary-value problems. Fedorov, V. E. // Journal of Mathematical Sciences;Apr2005, Vol. 126 Issue 6, p1658 

    Investigates the solvability of some problems that can be reduced to the Cauchy problem for a linear equation in a Hilbert space. Relatively p-sectorial operators and analytical semigroups; Polynomials of self-adjoint operators and relative spectra.

  • Abstract parabolic Cauchy problem in complex interpolation scales. Lopushansky, A. // Differential Equations;Dec2010, Vol. 46 Issue 12, p1799 

    We show that if the values of the inhomogeneous part of an autonomous parabolic linear equation belong to the complex interpolation scale associated with the sectorial operator of the equation, then there exists a unique classical solution of the Cauchy problem. This fact generalizes the...

Share

Read the Article

Courtesy of THE LIBRARY OF VIRGINIA

Sorry, but this item is not currently available from your library.

Try another library?
Sign out of this library

Other Topics