Results 211 to 220 of about 16,720 (245)

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.
J R L Webb
exaly   +3 more sources

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 and 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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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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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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Existence of Solutions for a Class of Nonlinear Evolution Inclusions with Nonlocal Conditions

Journal of Optimization Theory and Applications, 2013
This articles proves several theorems for the nonlinear first-order evolution inclusion with nonlocal condition \[ \begin{aligned} &\dot{x}(t)+A(t,x(t))+F(t,x(t))\ni f(t)\text{ on }I\equiv [ 0,T],\\ &x(0)=\varphi (x),\end{aligned}\tag{1} \] where \(A:I\times V\rightarrow V^{\ast }\), \(V\) is a dense subspace of the real separable Hilbert space \(H ...
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Existence of solutions and periodic solutions for nonlinear evolution inclusions

Rendiconti del Circolo Matematico di Palermo, 1999
The authors establish two existence theorems for evolution inclusions: the first for a periodic problem and the second for a Cauchy problem. It is stated a preliminary surjectivity result. More exactly, if \(Y\) is a reflexive, strictly convex Banach space, \(L: D(L)\subset Y\to Y^*\) be a linear densely defined maximal monotone operator and \(T: Y\to ...
Papageorgiou, Nikolaos S., Papalini, Francesca, Renzacci, Francesca   +2 more
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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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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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Nonlinear evolution inclusions with one-sided perron right-hand side

Journal of Dynamical and Control Systems, 2013
In this paper the authors study the evolution inclusion of the type \[ x'(t)\in A(x(t))+F(x(t)), \] where \(A\) is an \(m\)-dissipative operator and \(F\) is an upper hemicontinuous multifunction with non empty, convex and weakly compact values defined on a Banach space with a uniformly convex dual.
Cârjă, O., Donchev, T., Postolache, V.
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