Results 241 to 250 of about 193,561 (277)

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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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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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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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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Nonlocal problem for evolution inclusions with one-sided Perron nonlinearities

Revista de la Real Academia de Ciencias Exactas, Físicas y Naturales. Serie A. Matemáticas, 2018
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Bilal, S., Cârjă, O., Donchev, T., Lazu, A. I.   +3 more
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Convergence results for nonlinear evolution inclusions

1995
In the first part of this paper the authors consider the sequence of abstract Cauchy problems \((1)_n\) \(u'\in - \partial^- f(u)+ {\mathcal G}_n(u)\), \(u(0)= x_n\), \(x_n\in D(f)\), and the limit problem (1) \(u'\in -\partial^- f(u)+ {\mathcal G}(u)\), \(u(0)= \overline x\), \(\overline x\in D(f)\) (where \(\partial^- f\) is the Fréchet ...
CARDINALI, Tiziana, F. Papalini
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Global Solutions for Nonlinear Delay Evolution Inclusions with Nonlocal Initial Conditions

Set-Valued and Variational Analysis, 2012
Under suitable assumptions, the author obtains a sufficient condition for the existence of global \(C^{0}\)-solutions for the following nonlinear functional evolution equation \[ \left\{\begin{aligned} u^{\prime }(t)&\in Au(t)+f(t), \;t\in \mathbb{R}_{+}, \\ f(t)&\in F(t,u(t),u_{t}), \;t\in \mathbb{R}_{+}, \\ u(t)&=g(u)(t), \;t\in [ -\tau ,0], \end ...
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