Optimal Control and Relaxation of Nonlinear Elliptic Systems.
Existence Of Monotone, ψ-Minimal Solutions Of Differential Inclusions
Boundary value problems for evolution inclusions
On nonlinear, nonconvex evolution inclusions
We consider a nonlinear evolution inclusion driven by an m-accretive operator which generates an equicontinuous nonlinear semigroup of contractions. We establish the existence of extremal integral solutions and we show that they form a dense, -subset of the solution set of the original Cauchy problem. As an application, we obtain “bang-bang”’ type theorems for two nonlinear parabolic distributed parameter control systems.
Topological properties of the solution set of a class of nonlinear evolutions inclusions
In the paper we study the topological structure of the solution set of a class of nonlinear evolution inclusions. First we show that it is nonempty and compact in certain function spaces and that it depends in an upper semicontinuous way on the initial condition. Then by strengthening the hypothesis on the orientor field , we are able to show that the solution set is in fact an -set. Finally some applications to infinite dimensional control systems are also presented.
On the solution set of nonconvex subdifferential evolution inclusions
On nonconvex valued Volterra integral inclusions in Banach spaces
On the existence of -minimal viable solutions for a class of differential inclusions
Convergence theorems for set-valued conditional expectations
In this paper we prove two convergence theorems for set-valued conditional expectations. The first is a set-valued generalization of Levy’s martingale convergence theorem, while the second involves a nonmonotone sequence of sub -fields.
Boundary value problems and periodic solutions for semilinear evolution inclusions
We consider boundary value problems for semilinear evolution inclusions. We establish the existence of extremal solutions. Using that result, we show that the evolution inclusion has periodic extremal trajectories. These results are then applied to closed loop control systems. Finally, an example of a semilinear parabolic distributed parameter control system is worked out in detail.
An existence theorem for a class of nonlinear elliptic optimal control problems
We establish the existence of an optimal ``state-control'' pair for an optimal control problem of Lagrange type, monitored by a nonlinear elliptic partial equation involving nonmonotone nonlinearities.
Support prices for weakly maximal programs of a growth model with uncertainty
We consider an infinite dimensional, nonstationary growth model with uncertainty. Using techniques from functional analysis and the subdifferentiation theory of concave functions, we establish the existence of a supporting price system for a weakly maximal program.
On the properties of the solution set of nonconvex evolution inclusions of the subdifferential type
In this paper we consider nonconvex evolution inclusions driven by time dependent convex subdifferentials. First we establish the existence of a continuous selection for the solution multifunction and then we use that selection to show that the solution set is path connected. Two examples are also presented.
Properties of the solution of evolution inclusions driven by time dependent subdifferentials
In this paper we consider evolution inclusions driven by a time-dependent subdifferential. First we prove a relaxation result and then we use it to show that if the solution set is closed in a space of continuous functions, then the orientor field is almost everywhere convex valued.
On evolution inclusions associated with time dependent convex subdifferentials
Boundary value problems for evolution inclusions
Minimax control of nonlinear evolution equations
In this paper we study the minimax control of systems governed by a nonlinear evolution inclusion of the subdifferential type. Using some continuity and lower semicontinuity results for the solution map and the cost functional respectively, we are able to establish the existence of an optimal control. The abstract results are then applied to obstacle problems, semilinear systems with weakly varying coefficients (e.gȯscillating coefficients) and differential variational inequalities.
Existence of solutions for integrodifferential inclusions in Banach spaces
In this paper we examine nonlinear integrodifferential inclusions defined in a separable Banach space. Using a compactness type hypothesis involving the ball measure of noncompactness, we establish two existence results. One involving convex-valued orientor fields and the other nonconvex valued ones.
Random functional-differential inclusions with nonconvex right-hand side in a Banach space
On the separation of closed, convex sets
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