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PERTURBED NONLINEAR EVOLUTION INCLUSIONS IN BANACH SPACES
Acta Mathematica Scientia, 1995The paper concerns existence of integral solutions to the differential inclusion \(u'(t) \in Au(t) + F(t,u(t))\) where \(A\) is an \(m\)-dissipative operator which generates an equicontinuous semigroup on \(\overline {D(A)}\) and \((t,x) \to F(t,x)\) is a \((t,x)\)-measurable, \(x\)-lower semicontinuous set-valued map.
Xue, Xingmei, Song, Gouzhu
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Solutions of nonlinear evolution inclusions
Nonlinear Analysis: Theory, Methods & Applications, 1999Generalizing recent results by \textit{N. U. Ahmed} and \textit{X. Xiang} [Nonlinear Anal., Theory Methods Appl. 22, No. 1, 81-89 (1994; Zbl 0806.34051)], \textit{J. Berkovits} and \textit{V. Mustonen} [ibid. 27, No. 12, 1397-1405 (1996; Zbl 0894.34055)] and by \textit{H. Hirano} [ibid. 13, No.
W Bian, J R L Webb
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On the "bang-bang" principle for nonlinear evolution inclusions
NoDEA : Nonlinear Differential Equations and Applications, 1999The authors deal with the existence of solutions to an evolution inclusion of the form \[ x'(t) +A(t,x(t))\in{F(t,x(t))}\quad\text{a.e., }x(0)=x_{0}, \] in a Banach space, where the right-hand side is not necessarily convex-valued. It is an improvement of results by \textit{N. S. Papageorgiou} [Dyn. Syst. Appl. 2, No.
Tolstonogov, A. A., Tolstonogov, D. A.
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Properties of the Solution Set of Nonlinear Evolution Inclusions
Applied Mathematics and Optimization, 1997The paper deals with nonlinear nonautonomous evolution inclusions of the form \[ \dot x(t)+ A(t,x(t)) \in F(t,x(t)), \] a.e. on \(T\), \(x(0) =x_0\) defined on a Gelfand triple of spaces \((X,H,X^*)\). In Section 3 the authors provide conditions for the solution set to be an \(R_\delta\)-set, or path-connected in \(C(T,H)\).
Papageorgiou, N. S., Shahzad, N.
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