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Variable time-step $\theta$-scheme for nonlinear second order evolution inclusion

, 2017
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Second Order Nonlinear Evolution Inclusions II: Structure of the Solution Set

Acta Mathematica Sinica, English Series, 2005
The authors study the structural properties of the set of solutions of second-order evolution inclusions defined in the analytic framework of an evolution triple of spaces. Denoted by \(T\) the closed interval \([0,b]\) and by \((X,H,X^*)\) the evolution triple of spaces (\(H\) is a Hilbert space, \(X\) is a Banach space which is embedded compactly ...
Papageorgiou, Nikolaos S., Yannakakis, Nikolaos   +1 more
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Solutions of nonlinear evolution inclusions

Nonlinear Analysis: Theory, Methods & Applications, 1999
Generalizing 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.
Bian, W, Webb, J R L
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PERTURBED NONLINEAR EVOLUTION INCLUSIONS IN BANACH SPACES

Acta Mathematica Scientia, 1995
The 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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On the "bang-bang" principle for nonlinear evolution inclusions

NoDEA : Nonlinear Differential Equations and Applications, 1999
The 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 & Optimization, 1997
The 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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Optimal control of nonlinear evolution inclusions

Journal of Optimization Theory and Applications, 1990
We study the optimal control of nonlinear evolution inclusions. First, we prove the existence of admissible trajectories and then we show that the set that they form is relatively sequentially compact and in certain cases sequentially compact in an appropriate function space. Then, with the help of a convexity hypothesis and using Cesari's approach, we
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Second Order Nonlinear Evolution Inclusions I: Existence and Relaxation Results

Acta Mathematica Sinica, English Series, 2005
The authors study second-order nonlinear nonmonotone evolution inclusions defined in the framework of an evolution triple of spaces. In particular, they consider the problem \[ \ddot{x}(t) +A(t,\dot{x}(t))+Bx(t) \in F(t,x(t),\dot{x}(t)) \text{ a.e. }t \in T=[0,b],\;x(0)=z_0,\;\dot{x}(0)=z_1 , \] where \(A:T \times X \to X^*\) is a nonlinear operator, \(
Papageorgiou, Nikolaos S., Yannakakis, Nikolaos   +1 more
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Necessary and Sufficient Conditions for Viability for Nonlinear Evolution Inclusions

Set-Valued Analysis, 2007
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Cârjă, Ovidiu, Necula, Mihai, Vrabie, Ioan I.   +2 more
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