On weak solution to a hyperbolic differential inclusion with nonmonotone discontinuous nonlinear term.
Optimal control of impulsive stochastic evolution inclusions
In this paper, we consider a class of infinite dimensional stochastic impulsive evolution inclusions driven by vector measures. We use stochastic vector measures as controls adapted to an increasing family of complete sigma algebras and prove the existence of optimal controls.
Optimal control of semilinear evolution inclusions via discrete approximations
Periodic and almost periodic solutions for multi-valued differential equations in Banach spaces.
Periodic problems and problems with discontinuities for nonlinear parabolic equations
In this paper we study nonlinear parabolic equations using the method of upper and lower solutions. Using truncation and penalization techniques and results from the theory of operators of monotone type, we prove the existence of a periodic solution between an upper and a lower solution. Then with some monotonicity conditions we prove the existence of extremal solutions in the order interval defined by an upper and a lower solution. Finally we consider problems with discontinuities and we show that...
Perturbation stochastique de processus de rafle
Lors de cet exposé, nous nous intéressons à l’étude de perturbations stochastiques de certaines inclusions différentielles du premier ordre : les processus de rafle par des ensembles uniformément prox-réguliers. Ce travail nous amène à combiner la théorie des processus de rafle et celle traitant de la reflexion d’un mouvement brownien sur la frontière d’un ensemble. Nous donnerons des résultats traitant du caractère bien-posé de ces inclusions différentielles stochastiques et de leur stabilité.
Properties of attainable sets of evolution inclusions and control systems of subdifferential type.
Representation of the set of mild solutions to the relaxed semilinear differential inclusion
We study the relation between the solutions set to a perturbed semilinear differential inclusion with nonconvex and non-Lipschitz right-hand side in a Banach space and the solutions set to the relaxed problem corresponding to the original one. We find the conditions under which the set of solutions for the relaxed problem coincides with the intersection of closures (in the space of continuous functions) of sets of δ-solutions to the original problem.
Second order difference inclusions of monotone type
The existence of anti-periodic solutions is studied for a second order difference inclusion associated with a maximal monotone operator in Hilbert spaces. It is the discrete analogue of a well-studied class of differential equations.
Second-Order Viability Problem: A Baire Category Approach
The paper deals with the existence of viable solutions to the differential inclusion ẍ(t) ∈ f(t,x(t)) + ext F(t,x(t)), where f is a single-valued map and ext F(t,x) stands for the extreme points of a continuous, convex and noncompact set-valued mapping F with nonempty interior.
Second-order viability result in Banach spaces
We show the existence result of viable solutions to the second-order differential inclusion ẍ(t) ∈ F(t,x(t),ẋ(t)), x(0) = x₀, ẋ(0) = y₀, x(t) ∈ K on [0,T], where K is a closed subset of a separable Banach space E and F(·,·,·) is a closed multifunction, integrably bounded, measurable with respect to the first argument and Lipschitz continuous with respect to the third argument.
Semicontinuous differential inclusions
Semilinear Neutral Functional Integrodifferential Inclusions
Some quasivariational problems with memory
This note deals with a class of abstract quasivariational evolution problems that may include some memory effects. Under a suitable monotonicity framework, we provide a generalized existence result by means of a fixed point technique in ordered spaces. Finally, an application to the modeling of generalized kinematic hardening in plasticity is discussed.
The periodic problem for semilinear differential inclusions in Banach spaces
Sufficient conditions on the existence of periodic solutions for semilinear differential inclusions are given in general Banach space. In our approach we apply the technique of the translation operator along trajectories. Due to recent results it is possible to show that this operator is a so-called decomposable map and thus admissible for certain fixed point index theories for set-valued maps. Compactness conditions are formulated in terms of the Hausdorff measure of noncompactness.
Topological properties of solution sets for functional differential inclusions governed by a family of operators.
Topological structure of solution sets of differential inclusions: the constrained case.
Variational homotopy perturbation method for solving higher dimensional initial boundary value problems.
Variational inclusions for a Sturm-Liouville type differential inclusion
We establish several variational inclusions for solutions of a nonconvex Sturm-Liouville type differential inclusion on a separable Banach space.
Viability problem with perturbation in Hilbert space.