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1.
For a conflict-controlled dynamical system whose motion is described by neutraltype functional differential equations in Hale’s form and for a quality index that evaluates the motion history realized up to the terminal instant of time, we consider a differential game in the class of control-with-guide strategies. We construct an approximating differential game in the class of pure positional strategies in which the motion of a conflict-controlled system is described by ordinary differential equations and the quality index is terminal. We show that the value of the approximating game gives the value of the original game in the limit, and that the optimal strategies in the original game can be constructed by using the optimal motions of the approximating game as guides.  相似文献   

2.
Let F=F(t,x) be a bounded, Hausdorff continuous multifunction with compact, totally disconnected values. Given any y0F(t0,x0), we show that the differential inclusion has a globally defined classical solution, with x(t0)=x0, .  相似文献   

3.
The existence of a generalized solution with continuous derivativesu x ,u y is proved for the differential inclusionu xy F(x, y, u) with a nonconvex right-hand side satisfying the Lipschitz conditioninx, y, andu.Translated from Ukrainskii Matematicheskii Zhurnal, Vol. 47, No. 4, pp. 531–534, April, 1995.  相似文献   

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We study the properties of the trajectories of a differential inclusion with unbounded measurable–pseudo-Lipschitz right-hand side that takes values in a separable Banach space and consider the problem of minimizing a functional over the set of trajectories of such a differential inclusion on an interval. We obtain necessary optimality conditions in the form of Euler–Lagrange differential inclusions for a problem with free right end.  相似文献   

6.
The concept of an integral manifold of a system of differential equations with a random right-hand side is introduced. The problem of the existence of an integral manifold of a certain class of differential equations in a Banach space and several of its properties are investigated.Translated from Ukrainskii Matematicheskii Zhurnal, Vol. 44, No. 1, pp. 17–21, January, 1992.  相似文献   

7.
We show that the classical algorithm for finding a particular solution of a scalar linear differential equation can be applied to linear differential equations with bounded operator coefficients in a Banach space.  相似文献   

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The paper studies an evolution inclusion in a separable Hilbert space whose right-hand side contains the subdifferential of a proper convex lower semicontinuous function of time and a set-valued perturbation. Together with this inclusion, an inclusion with convexified perturbation values is considered. The existence and density of the solution set of the initial inclusion in the closure of the solution set of the inclusion with convexified perturbation are proved. This property is usually called relaxation. Traditional assumptions for relaxation theorems are the compactness property of the convex function and the boundedness of the perturbation. In the present paper, such assumptions are not made. Assumptions for subdifferential inclusions described by polyhedral sweeping processes and variational inequalities with time-dependent obstacles and constraints are specified.  相似文献   

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We prove two existence theorems for random differential inclusions defined in a separable Banach space. One is about differential inclusions defined on all of the Banach space X and the other for differential inclusion defined on a closed convex subset K. Both theorems are proved through the use of analogous deterministic results, which we also include, and techniques from the theory of measurable multifunctions.  相似文献   

13.
We obtain existence theorems and Filippov-Wa?ewski type relaxation theorems for differential inclusions in Banach spaces with measurable-pseudo-Lipschitz right-hand side. For the solution sets of these differential inclusions, we also describe some properties that extend classical theorems on continuous dependence and on differentiation of solutions with respect to initial data.  相似文献   

14.
In this paper we investigate the existence of solutions for first and second order nonresonance impulsive functional differential inclusions. We shall rely on the Schaefer's fixed point theorem combined with a selection theorem due to Bressan and Colombo for lower semicontinuous multivalued maps with nonempty closed and decomposable values.  相似文献   

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In this paper, Schaefer's fixed point theorem combined with a selection theorem due to Bressan and Colombo is used to investigate the existence of solutions for the first- and second-order functional and neutral functional integrodifferential inclusions with lower semicontinuous and nonconvex-valued right-hand side.  相似文献   

17.
In a Banach space E, we study the equation 1 $$ u''(t) + Bu'(t) + Cu(t) = f(t), 0 \leqslant t < \infty $$ , where f(t) ∈ C([0,∞);E), B,CN(E), and N(E) is the set of closed unbounded linear operators from E to E with dense domain in E. We find a two-parameter family of solutions of Eq. (1) in two cases: (a) the operator discriminant D = B 2 ? 4C of Eq. 1 is zero; (b) D = F 2, where F is some operator in N(E). We suggest a method for increasing the smoothness of such solutions by imposing more restrictive conditions on the input data W = (B,C,f(t)) and the parameters x 1, x 2E.  相似文献   

18.
A. V. Zuev 《Mathematical Notes》2006,79(3-4):518-527
A new version of the method of translation along trajectories, which does not require the uniqueness of the solution of the Cauchy problem, is applied to the proof of the existence theorem for vector-valued periodic solutions of ordinary differential equations of first and second order. This result is applicable to equations and differential inclusions with discontinuous right-hand side. Several applications of the theorems proved in this paper are considered in cases which are not covered by the classical theory of ordinary differential equations with continuous right-hand side and equations with right-hand side satisfying the Carathéodory conditions.  相似文献   

19.
A method for the investigation of differential equations with a nonclassical right-hand side [1] is applied to the study of the higher-order differentiability of solutions of differential equations with discontinuous right-hand sides with respect to the initial data. We use results from the theory of differential equations with pulse influence [2].Translated from Ukrainskii Matematicheskii Zhurnal, Vol. 45, No. 12, pp. 1587–1594, December, 1993.  相似文献   

20.
In this paper, an existence theorem for a certain hyperbolic differential inclusions in Banach algebras is proved under the mixed Lipschitz and Carathéodory conditions. The existence of extremal solutions for Carathéodory as well as discontinuous hyperbolic differential inclusions is also proved under certain monotonicity conditions.  相似文献   

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