Results 241 to 250 of about 67,156 (272)
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Necessary conditions for functional differential inclusions
Applied Mathematics & Optimization, 1996The authors derive a necessary optimality condition in the form of a Hamiltonian inclusion for functional differential inclusions with finite-dimensional terminal constraints. A number of technical difficulties have to be solved in order to deal with the state space of continuous functions. For control problems, an adjoint equation is derived.
Clarke, F. H., Wolenski, P. R.
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On the Theory of Functional-Differential Inclusion of Neutral Type
gmj, 2002Abstract A Cauchy problem for a functional-differential inclusion of neutral type with a nonconvex right-hand side is investigated. Questions of the solvability of such a problem are considered, estimates analogous to the Filippov's estimates are obtained and the density principle is proved.
Bulgakov, A. I., Vasilyev, V. V.
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Monotone trajectories of differential inclusions and functional differential inclusions with memory
Israel Journal of Mathematics, 1981The paper gives a necessary and sufficient condition for the existence of monotone trajectories to differential inclusionsdx/dt ∈S[x(t)] defined on a locally compact subsetX ofRp, the monotonicity being related to a given preorder onX. This result is then extended to functional differential inclusions with memory which are the multivalued case to ...
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Differential Inclusions and Monotonicity Conditions for Nonsmooth Lyapunov Functions
Set-Valued Analysis, 2000The authors study the differential inclusion \(x'\in F(x)\), \(x\in\mathbb{R}^n\), \(x(0)= x_0\in \mathbb{R}^n\), where \(F\) is a set-valued map defined in \(\mathbb{R}^n\) with compact values, together with a function \(F: \mathbb{R}^n\to \mathbb{R}\) such that either \(F\) is locally Lipschitz continuous (in the Hausdorff sense) and \(V\) is lower ...
BACCIOTTI, Andrea +2 more
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Differential Equations, 2007
The functional differential inclusion with delay \[ \dot{x}\in F(t,x_t(\cdot)),\quad x_{t_0}(\cdot)=\varphi_0(\cdot) \] is considered. Here, \(x_t(\cdot)\in C_r, x_t(\theta)=x(t+\theta), -\tau\leq\theta\leq 0\), and \(\varphi(\cdot)\in C_r\) is the initial function.
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The functional differential inclusion with delay \[ \dot{x}\in F(t,x_t(\cdot)),\quad x_{t_0}(\cdot)=\varphi_0(\cdot) \] is considered. Here, \(x_t(\cdot)\in C_r, x_t(\theta)=x(t+\theta), -\tau\leq\theta\leq 0\), and \(\varphi(\cdot)\in C_r\) is the initial function.
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Learning potential function and differential inclusion
[Proceedings 1992] IJCNN International Joint Conference on Neural Networks, 2003A unified mathematical theory of neural learning is presented. A learning potential function for a neural network is introduced, and a novel dynamical system approach to nondifferentiable, global optimization problems is proposed. A differential inclusion (DI) for finding a global minimum of a learning potential function is derived.
M. Xiong, P. Wang
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The Solution Set to BVP for Some Functional Differential Inclusions
Set-Valued Analysis, 1998The authors show that the set of solutions to the multivalued boundary value problem \(x'(t) \in A(t)x(\alpha (t))+ \lambda F(t, x(\beta (t))),\) \(Lx=\theta\), forms a nonempty infinite-dimensional AR-space for sufficiently small \(\lambda\).
Augustynowicz, A. +2 more
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Singularly perturbed functional-differential inclusions
Set-Valued Analysis, 1995The following singularly perturbed system of functional differential inclusions with state constraints is considered: \[ (x'(t), \varepsilon y'(t))\in F(t, x(t), y(t), x_t, y_t),\quad x(t)\in K_1,\;y(t)\in K_2, \] where \(K_1\), \(K_2\) are closed convex sets and \(x\in \mathbb{R}^n\), \(y\in \mathbb{R}^m\).
Donchev, Tzanko, Slavov, Iordan
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Estimates of support functions of averaged differential inclusions
Mathematical Notes of the Academy of Sciences of the USSR, 1991See the review in Zbl 0743.34027.
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Inclusion of Zeros of Nowhere Differentiable n-Dimensional Functions
Reliable Computing, 1997The author describes a method to calculate verified error bounds for the zeros of \(n\)-dimensional nonlinear nowhere differentiable continuous functions. An infinite number of zeros can be found within the calculated error bounds. To allow for computer applications interval operations may replace the power set operations. Numerical examples worked out
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