Nonlocal evolution inclusions under weak conditions
type: Item
instance of: scholarly article
title: Nonlocal evolution inclusions under weak conditions
zbMATH Open document ID: 1458.34112
author: Sh. Bilal
author: T. Donchev
author: Nasir Javaid
author: A. I. Lazu
author: Ovidiu Cârjă
published in: Advances in Difference Equations
publication date: 2019-02-05T00:00:00Z
review text: The authors investigate evolution inclusions given by multivalued perturbations of \(m\)-dissipative operators with nonlocal initial conditions. The system has the form \[ \dot{y}(s)\in Ay(s)+F(s,y(s)),\, s\in I=[t_0,T],\, y_0(t_0)=g(y(\cdot)), \] where \(A:D(A)\subset X\rightrightarrows X\) is a \(m\)-dissipative operator, \(F:I\times X\rightrightarrows X\) a multifunction, mapping \(g: C(I,X)\to \overline{D(A)}\), and \(X\) is a Banach space with uniformly convex dual. The authors prove the existence of solutions assuming that \(F(s,\cdot)\) is one-sided Lipschitz, which is weaker than the commonly used Lipschitz condition. To this end the corresponding Cauchy problem is studied. Next, they relax the growth conditions on \(g(\cdot)\) and it seems that the assumptions are weaker and more flexible. Notice also that even if \(F(s,\cdot )\) is Lipschitz, then either the one-sided Lipschitz constant or some function is in general smaller than the Lipschitz one. The existence result concerns the multipoint problems that cover periodic and antiperiodic cases. Some examples illustrate the applicability of the results.
reviewed by: Dimitar A. Kolev
Mathematics Subject Classification ID: 34G25
Mathematics Subject Classification ID: 34B10
Mathematics Subject Classification ID: 34C25
zbMATH DE Number: 7012793
zbMATH Keywords: m-dissipative evolution inclusions
zbMATH Keywords: nonlocal initial conditions
zbMATH Keywords: one-sided Lipschitz condition
MaRDI profile type: Publication
full work available at URL: s13662-018-1858-6
OpenAlex ID: W2898580907
cites work: Nonlocal \(m\)-dissipative evolution inclusions in general Banach spaces
cites work: Multivalued evolution equations with nonlocal initial conditions in Banach spaces
cites work: Nonlinear Differential Equations of Monotone Types in Banach Spaces
cites work: Q5658694
cites work: Multivalued perturbations of \(m\)-accretive differential inclusions
cites work: Delay differential evolutions subjected to nonlocal initial conditions
cites work: Q3441590
cites work: Nonlinear evolution inclusions: topological characterizations of solution sets and applications
cites work: Filippov-Pliss lemma and \(m\)-dissipative differential inclusions
cites work: Q3147027
cites work: Stability and Euler Approximation of One-sided Lipschitz Differential Inclusions
cites work: Q4942053
cites work: The poles and growth of solutions of systems of complex difference equations
cites work: Q3904867
cites work: Q5744750
cites work: A class of nonlinear evolution equations subjected to nonlocal initial conditions
cites work: Nonlinear partial differential equations with applications
cites work: Q4332942
cites work: Existence in the large for nonlinear delay evolution inclusions with nonlocal initial conditions
cites work: Global solutions for nonlinear delay evolution inclusions with nonlocal initial conditions
cites work: Q3609633
cites work: Existence and asymptotic properties of solutions of nonlinear multivalued differential inclusions with nonlocal conditions
DOI: 10.1186/S13662-018-1858-6
description: scientific article; zbMATH DE number 7012793