Viable control for uncertain nonlinear dynamical systems described by differential inclusions

In this paper, we will study the viable control problem for a class of uncertain nonlinear dynamical systems described by a differential inclusion. The goal is to construct a feedback control such that all trajectories of the system are viable in a map. Moreover, for any initial states no viable in the map, under the feedback control, all solutions of the system are steered to the map with an exponential convergence rate and viable in the map after a finite time T. In this case, an estimate of the time T of all trajectories attaining the map is given. In the nanomedicine system, an example inspired from cerebral embolism and cerebral thrombosis problems illustrates the use of our main results.     

On boundary-value problems for second order perturbed differential inclusions

This article studies the existence of solutions to boundary-value problems for second order multi-valued perturbed differential inclusions under the mixed Lipschitz and Carathéodory conditions. The existence of extremal solutions is also obtained under certain monotonicity conditions and the weaker nonconvexity conditions for multi-valued functions.     

Existence of solutions and periodic solutions for nonlinear evolution inclusions

In this paper we consider nonlinear-dependent systems with multivalued perturbations in the framework of an evolution triple of spaces. First we prove a surjectivity result for generalized pseudomonotone operators and then we establish two existence theorems: the first for a periodic problem and the second for a Cauchy problem. As applications we work out in detail a periodic nonlinear parabolic partial differential equation and an optimal control problem for a system driven by a nonlinear parabolic equation.     

On periodic solutions of even-order ordinary differential equations

Optimal in a certain sense sufficient conditions are given for the existence and uniqueness of ω-periodic solutions of the nonautonomous ordinary differential equation u ^(2m) =f(t,u,...,u ^(m-1) ), where the function f:ℝ×ℝ ^m →ℝ is periodic with respect to the first argument with period ω. Received: December 21, 1999; in final form: August 12, 2000?Published online: October 2, 2001     

Impulsive mild solutions for semilinear differential inclusions with nonlocal conditions in Banach spaces

In this paper we deal with the existence of impulsive mild solutions for semilinear differential inclusions with nonlocal conditions, where the linear part generates an evolution system and the nonlinearity satisfies the lower Scorza-Dragoni property. Our theorems extend the existence propositions proved by Fan in 2010. An example is presented.     

Impulsive semilinear differential inclusions: Topological structure of the solution set and solutions on non-compact domains

This paper deals with an impulsive Cauchy problem governed by the semilinear evolution differential inclusion x^′(t)∈A(t)x(t)+F(t,x(t))$x^{\prime }\left(t\right)\in A\left(t\right)x\left(t\right)+F(t,x\left(t\right))$, where _{{A(t)}t∈[0,b]}${\left\{A\left(t\right)\right\}}_{t\in [0,b]}$ is a family of linear operators (not necessarily bounded) in a Banach space E$E$ generating an evolution operator and F$F$ is a Carathéodory type multifunction. First a theorem on the compactness of the set of all mild solutions for the problem is given. Then this result is applied to obtain the existence of mild solutions for the impulsive Cauchy problem defined on non-compact domains.     

Periodic solutions to impulsive differential inclusions with constraints

The existence of a periodic solution to an impulsive differential inclusion being invariant with respect to a non-convex set of state constraints is established by the use a Lefschetz type fixed-point theorem for set-valued maps.     

Existence and controllability results for impulsive partial functional differential inclusions

In this paper we prove the existence and the controllability of mild and extremal mild solutions for first-order semilinear densely defined impulsive functional differential inclusions in separable Banach spaces with local and nonlocal conditions.     

Analytic solutions to integral equations in the complex domain

Schauder's fixed point theorem and the Leray–Schauder alternative are used to establish the existence of analytic solutions to integral equations in the complex domain.     

Compact,convex sets in R n and a new banach lattice. II.- Application: An approximation problem.

We develop a calculus structure in the Banach lattice introduced in a preceding paper, having in mind an approximation problem appearing in non-smooth optimization. We show that the essential results depend as much on the order structure as on the analytical one.     

Lp-Perturbation of Linear Functional Differential Equations

 For a class of retarded linear differential equations with solutions of exponential form, it is shown that L ^p -perturbations leave the solutions of the same form. As a particular example, the asymptotic integration of a class of differential equations is obtained. (Received 10 August 1998)     

Some new results on functions in C(X) having their support on ideals of closed sets

Abstract

For any ideal of closed sets in X, let be the family of those functions in C(X) whose support lie on . Further let contain precisely those functions f in C(X) for which for each ? > 0, {x ∈ X: |f (x)| ≥ ?} is a member of . Let stand for the set of all those points p in βX at which the stone extension f^? for each f in is real valued. We show that each realcompact space lying between X and βX is of the form if and only if X is pseudocompact. We find out conditions under which an arbitrary product of spaces of the form locally- or almost locally-, becomes a space of the same form. We further show that is a free ideal (essential ideal) of C(X) if and only if is a free ideal (essential ideal) of when and only when X is locally- (almost locally-). We address the problem, when does or become identical to the socle of the ring C(X). The results obtained turn out to imply a special version of the fact obtained by Azarpanah corresponding to the choice ≡ the ideal of compact sets in X. Finally we observe that the ideals of the form of C(X) are no other than the z^?-ideals of C(X).     

Unbounded solutions of differential equations of second order

In this paper, the existence of unbounded solutions for the following nonlinear asymmetric oscillator

On the existence of periodic solutions for differential inclusions

In this paper we study the existence of periodic solutions for differential inclusions. We prove existence theorems under various sets of hypotheses for both the nonconvex and convex problems. Also we show the existence of extreme solutions. Some feedback control systems are also considered.     

Positive periodic solutions of a periodic survival red blood cell model

By using the continuation theorem of coincidence degree theory by Gaines and Mawhin, a sufficient and realistic condition is obtained for the existence of a periodic survival red blood cell model.