Solutions Of Functional Differential Inclusions Research Articles

Functional differential inclusions with maximal monotone operators and nonconvex perturbations

In this paper, we study the existence of solutions for functional differential inclusions governed by time-dependent maximal monotone operators with nonconvex perturbations depending on all the variables.

Интегральные направляющие потенциалы в задаче об асимптотическом поведении решений функционально-дифференциальных включений

Интегральные направляющие потенциалы в задаче об асимптотическом поведении решений функционально-дифференциальных включений

Existence of monotone solutions for functional differential inclusions without convexity

Existence of monotone solutions for functional differential inclusions without convexity

Method of generalized integral guiding functions in the problem of the existence of periodic solutions for functional-differential inclusions

We suggest new methods for the solution of a periodic problem for a nonlinear object described by the differential inclusion x′(t) ∈ F(t, xt) under the assumption that the multimapping F has convex compact values and satisfies the upper Caratheodory conditions. We also study the case in which this multimapping is not convex-valued but is normal. The class of normal multimappings includes, for example, bounded almost lower semicontinuous multimappings with compact values and mappings satisfying the Caratheodory conditions. In both cases, a generalized integral guiding function is used to study the problem.

Effects of bounded and unbounded leakage time-varying delays in memristor-based recurrent neural networks with different memductance functions

This paper is concerned with the problem of μ-stability analysis of memristor-based recurrent neural networks with the effects of bounded and unbounded leakage time-varying delays. A new idea of μ-stability analysis of neural networks is given first, then by means of the linear matrix inequality (LMI) approach, stability criteria are presented. Two types of memductance functions is used to derive the proposed stability results. Obviously, the memristive neural network with different memductance functions is a state-dependent switched system or a state-dependent continuous system, which is the generalization of those for conventional artificial neural networks. Under the framework of Filippov solutions, μ-stability analysis of solutions for functional differential inclusions and memristor-based neural networks can be guaranteed by constructing suitable Lyapunov–Krasovskii functionals, suitable inequalities and LMIs. The dynamic analysis in this paper utilizes the theory of set-valued maps and functional differential equations with discontinuous right-hand sides of Filippov type. Leakage time-varying delay is considered in this paper to be bounded, unbounded and differentiable. Taking into account of the information of the neuron activation functions and unbounded time-varying delays, several improved results have been obtained in terms of LMIs and these are tested by MATLAB LMI toolbox. The model based on the memristor widens the relevance scope for the design of neural networks, and the new effective results also enrich the toolbox for the qualitative analysis of neural networks. Finally, numerical examples are provided to demonstrate the effectiveness of the proposed theoretical results.

Convex Sweeping Processes with Noncompact Perturbations and with Delay in Banach Spaces

We prove two results concerning the existence of solutions for functional differential inclusions that are governed by sweeping processes, with noncompact valued perturbations in Banach spaces. Indeed, we have two goals. The first is to give a technique that allows considering sweeping processes with noncompact valued perturbations and associated with a multivalued function depending on time. The second is to give a technique to overcome the arising problem from the nonlinearity of the normalized mappings, when we deal with sweeping processes with noncompact valued perturbations and associated with a multivalued function depending on time and state.

О методе негладкой интегральной направляющей функции в задаче о существовании периодических решений функционально-дифференциальных включений с невыпуклой правой частью

О методе негладкой интегральной направляющей функции в задаче о существовании периодических решений функционально-дифференциальных включений с невыпуклой правой частью

Functional differential inclusions and dynamic behaviors for memristor-based BAM neural networks with time-varying delays

In this paper, we formulate and investigate a class of memristor-based BAM neural networks with time-varying delays. Under the framework of Filippov solutions, the viability and dissipativity of solutions for functional differential inclusions and memristive BAM neural networks can be guaranteed by the matrix measure approach and generalized Halanay inequalities. Then, a new method involving the application of set-valued version of Krasnoselskii’ fixed point theorem in a cone is successfully employed to derive the existence of the positive periodic solution. The dynamic analysis in this paper utilizes the theory of set-valued maps and functional differential equations with discontinuous right-hand sides of Filippov type. The obtained results extend and improve some previous works on conventional BAM neural networks. Finally, numerical examples are given to demonstrate the theoretical results via computer simulations.

Fractional functional differential inclusions with finite delay

In this paper, we present fractional versions of the Filippov theorem and the Filippov–Wazewski theorem, as well as an existence result, compactness of the solution set and Hausdorff continuity of operator solutions for functional differential inclusions with fractional order, D α y ( t ) ∈ F ( t , y t ) , a.e. t ∈ [ 0 , b ] , 0 < α < 1 , y ( t ) = ϕ ( t ) , t ∈ [ − r , 0 ] , where J = [ 0 , b ] , D α is the standard Riemann–Liouville fractional derivative, and F is a set-valued map.

Generalized Solutions of Functional Differential Inclusions

We consider the initial value problem for a functional differential inclusion with a Volterra multivalued mapping that is not necessarily decomposable inL1n[a,b]. The concept of the decomposable hull of a set is introduced. Using this concept, we define a generalized solution of such a problem and study its properties. We have proven that standard results on local existence and continuation of a generalized solution remain true. The question on the estimation of a generalized solution with respect to a given absolutely continuous function is studied. The density principle is proven for the generalized solutions. Asymptotic properties of the set of generalized approximate solutions are studied.

A method of upper and lower solutions for functional differential inclusions

In this paper, a fixed point theorem for condensing maps combined with upper and lower solutions are used to investigate the existence of solutions for first order functional differential inclusions.

Periodic solutions and equilibrium states for functional-differential inclusions with nonconvex right-hand side

In this paper, we present a general existence theorem for periodic solutions for functional differential inclusions with nonconvex right-hand side. As an application, we prove that for a multivalued system with nonconvex right-hand side, permanence implies the existence of a pre-equilibrium state, which answers an open problem proposed by Hutson.

Extremal Solutions of Functional Differential Inclusions

In this paper, we prove the existence of extremal solutions of functional differential inclusions, in particular, we can prove the existence of extremal solutions of differential inclusions without assuming that the right-hand side multifunction is jointly upper semi-continuous.

Existence of solutions of functional differential inclusions

We prove the existence of solutions of a functional differential inclusion. By using the variation of parameters formula we convert the functional differential inclusion into an integral inclusion and prove the existence of a fixed point of the set‐valued mapping with the help of the Kakutani‐Bohnenblust‐Karlin fixed point theorem.

Periodic solutions of functional differential inclusions and fixed points of σ-selectionable correspondences

Periodic solutions of functional differential inclusions and fixed points of σ-selectionable correspondences

Topological properties of the sets of solutions for functional differential inclusions

Topological properties of the sets of solutions for functional differential inclusions