ANTI-PERIODIC SOLUTIONS FOR DIFFERENTIAL INCLUSIONS IN BANACH SPACES AND THEIR APPLICATIONS

We deal with anti-periodic problems for differential inclusions with nonmonotone perturbations. The main tools in our study are the maximal monotone property of the derivative operator with anti-periodic conditions and the theory of pseudomonotone perturbations of maximal monotone mappings. We then apply our results to evolution hemivariational inequalities and parabolic equations with nonmonotone discontinuities, which generalize and extend previously known theorems.

Solvability of Impulsive Neutral Functional Differential Inclusions in Banach Spaces

Impulsive neutral differential inclusions play an important role in characterizing many social, physical and engineering problems, and the existence of solutions for the initial value problem in Banach spaces has been extensively studied. However, in most cases, the nonlinear term on the right-hand side of differential inclusions has to satisfy the compact or continuous assumptions. The object of this paper is to study the existence of solutions to the initial value problems of the first and second order impulsive neutral functional differential inclusions in Banach spaces under some weaker conditions, where the nonlinear term on the right-hand side does not necessarily satisfy the compact and continuous assumptions. Based on a fixed point theorem for discontinuous multivalued increasing operators, the results are obtained by means of the partial ordering method and measure of noncompactness.

Controllability of Fractional Order Stochastic Differential Inclusions with Fractional Brownian Motion in Finite Dimensional Space

In this paper,sufficient conditions are formulated for controllability of fractional order stochastic differential inclusions with fractional Brownian motion(f Bm) via fixed point theorems,namely the Bohnenblust-Karlin fixed point theorem for the convex case and the Covitz-Nadler fixed point theorem for the nonconvex case.The controllability Grammian matrix is defined by using Mittag-Leffler matrix function.Finally,a numerical example is presented to illustrate the efficiency of the obtained theoretical results.

CONTINUOUS SELECTIONS OF SOLUTION SETS OF FRACTIONAL INTEGRO-DIFFERENTIAL INCLUSIONS

Using Bressan-Colombo results, concerning the existence of continuous selections of lower semicontinuous multifunctions with decomposable values, we prove a continuous version of Filippov＇s theorem for a fractional integro-differential inclusion involving Caputo＇s fractional derivative. This result allows us to obtain a continuous selection of the solution set of the problem considered.

Existence of solutions for implicit fuzzy differential inclusions

A class of implicit fuzzy differential inclusions （IFDIs） are introduced and studied. Some existence theorems under different conditions are proved with the selection theorems for the open situation and the closed situation, respectively. A viable solution for a closed IFDI is proved to exist under the tangential condition. As an application, an implicit fuzzy differential equation, which comes from the drilling dynamics in petroleum engineering, is analyzed numerically. The obtained results can improve and extend some known results for fuzzy differential inclusions （FDIs） and fuzzy differential equations （FDEs）, which might be helpful in the analysis of fuzzy dynamic systems.

ON THE PERIODIC SOLUTIONS OF DIFFERENTIAL INCLUSIONS AND APPLICATIONS

The periodic problem of evolution inclusion is studied and its results are used to establish existence theorems of periodic solutions of a class of semi_linear differential inclusion.Also existence theorem of the extreme solutions and the strong relaxation theorem are given for this class of semi_linear differential inclusion. An application to some feedback control systems is discussed.

EXISTENCE OF SOLUTIONS FORP ARABOLIC TYPE EVOLUTION DIFFERENTIAL INCLUSIONS AND THE PROPERTY OF THE SOLUTION SET

In this paper, parabolic type differential inclusions with time dependent ape considered and this problem is related to the study of the nonlinear distributed parameter central systems. An existence theorem of mild-solutions is proved, and a property of the solution set is given. The directions and the results by J.P. Aubin et al. are generalized and improved.

A Kind of Nonconvex-valued Functional Differential Inclusions Problems

In this paper,we consider nonconvex-valued functional differential inclusions with nonlinear semigroups in Banach spaces,the existence of the integral solutions is proved.

Existence of Periodic Solutions for Differential Inclusions

This paper deals with the periodic solution theory to differential inclusions related to periodic optimal control problems. The results of Halanay and Yoshizawa are presented for multivalued systems.

Lyapunov stability and generalized invariance principle for nonconvex differential inclusions

This paper studies the system stability problems of a class of nonconvex differential inclusions. At first, a basic stability result is obtained by virtue of locally Lipschitz continuous Lyapunov functions. Moreover, a generalized invariance principle and related attraction conditions are proposed and proved to overcome the technical difficulties due to the absence of convexity. In the technical analysis, a novel set-valued derivative is proposed to deal with nonsmooth systems and nonsmooth Lyapunov functions. Additionally, the obtained results are consistent with the existing ones in the case of convex differential inclusions with regular Lyapunov functions. Finally, illustrative examples are given to show the effectiveness of the methods.

IMPULSIVE BOUNDARY VALUE PROBLEMS FOR STURM-LIOUVILLE TYPE DIFFERENTIAL INCLUSIONS

In this paper, the authors investigate the existence of solutions of impulsive boundary value problems for Sturm-Liouville type differential inclusions which admit non-convex-valued multifunctions on right hand side. Two results under weaker conditions are presented. The methods rely on a fixed point theorem for contraction multi-valued maps due to Covitz and Nadler and Schaefer＇s fixed point theorem combined with lower semi-continuous multi-valued operators with decomposable values.

Impulsive Boundary Value Problems for First-order Ordinary Differential Inclusions

In this paper, we investigate the existence of solutions for impulsive first order ordinary differential inclusions which admitting nonconvex valued right hand side. We present two classes of results. In the first one, we rely on a fixed point theorem for contraction multivalued maps due to Covitz and Nadler, and for the second one, we use Schacfer＇s fixed point theorem combined with lower semi-continuous multivalued operators with decomposable values under weaker conditions.

Uncertainty in public health models treated by differential inclusions

An application of differential inclusions in the epidemic spread models is presented.Some mostly used epidemic models are discussed here,and a brief survey of epidemic modeling is given.Most of the models are some modifications of the Susceptible–Infected–Recovered model.Simple simulations are carried out.Then,we consider the influence of some uncertain parameters.It is pointed out that the presence of some fluctuating model parameters can be treated by differential inclusions.The solution to such differential inclusion is given in the form of reachable sets for model variables.Here,we focus on the differential inclusion application rather than the model construction.

On Systems of Boundary Value Problems for Differential Inclusions

Herein we consider the existence of solutions to second-order, two-point boundary value problems （BVPs） for systems of ordinary differential inclusions. Some new Bernstein-Nagumo conditions are presented that ensure a priori bounds on the derivative of solutions to the differential inclusion. These a priori bound results are then applied, in conjunction with appropriate topological methods, to prove some new existence theorems for solutions to systems of BVPs for differential inclusions. The new conditions allow of the treatment of systems of BVPs without growth restrictions.

NONDENSELY DEFINED IMPULSIVE NEUTRAL FUNCTIONAL DIFFERENTIAL INCLUSIONS WITH NONLOCAL CONDITIONS

In this paper,using a fixed point theorem for condensing multi-valued maps,we investigate the existence of integral solutions to a class of nondensely defined neutral evolution impulsive differential inclusions with nonlocal conditions in Banach spaces.

(k, n-k) CONJUGATE MULTI-POINT BOUNDARY VALUE PROBLEMS FOR A CLASS OF HIGHER-ORDER DIFFERENTIAL INCLUSIONS

In this paper a fixed point theorem for contracting maps is used to investigate the existence of solutions to a class of higher-order differential inclusions with (k, n-k) conjugate multi-point boundary value problem.

VIABILITY CRITERIA FOR DIFFERENTIAL INCLUSIONS

A method of verifying the viability criterion at a given point for a region with nonsmooth boundary, which is expressed by a quasidifferentiabl function, under a differential inclusion which is a convex hull of finitely many functions, is proposed. By this method, determining the viability is transformed into solving a number of systems of linear inequalities, or equivalently solving a number of linear programming problems. For the other differential inclusion, called the generalized convex process, it is shown that viability condition holds for a polytope if and only if it holds at all of its vertices. This result is an extension of corresponding one for a linear control system.

Existence Results for Functional Differential Inclusions with Infinite Delay

The aim of the present paper is to investigate the existence of solutions to functional differential inclusions with infinite delay in Banach spaces. A relevant set of phase space axioms is proposed. The main tools used in this paper are certain fixed point theorems based on the setcontraction theory.

MULTIVALUED PERTURBATION TO NONLINEAR DIFFERENTIAL INCLUSIONS WITH MEMORY IN BANACH SPACES

The authors give the existence results to the nonlinear differential inclusion u'(t) ∈ Au(t) +F(t,ut), where A is a ganerator of equicontinuous semigroup and F is multivalued.

Existence Theorems for Periodic Differential Inclusions in IR^N

We study the periodic problem for differential inclusions in R^N.First we look for extremal periodicsolutions.Using techniques from multivalued analysis and a fixed point argument we establish an existencetheorem under some general hypotheses.We also consider the“nonconvex periodic problem”under lowersemicontinuity hypotheses,and the“convex periodic problem”under general upper semicontinuity hypotheseson the multivalued vector field.For both problems,we prove existence theorems under very general hypotheses.Our approach extends existing results in the literature and appear to be the most general results on the nonconvexperiodic problem.