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.
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.
Random functional-differential inclusions with nonconvex right-hand side in a Banach space
Boundary value problems for evolution inclusions
On the separation of closed, convex sets
On the existence of -minimal viable solutions for a class of differential inclusions
On evolution inclusions associated with time dependent convex subdifferentials
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.
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 integral inclusions of Volterra type in Banach spaces
On the solution set of nonconvex subdifferential evolution inclusions
On nonconvex valued Volterra integral inclusions in Banach spaces
Convexity of the orientor field and the solution set of a class of evolution inclusions
Existence of solutions for hyperbolic differential inclusions in Banach spaces
In this paper we examine nonlinear hyperbolic inclusions in Banach spaces. With the aid of a compactness condition involving the ball measure of noncompactness we prove two existence theorems. The first for problems with convex valued orientor fields and the second for problems with nonconvex valued ones.
Parametrized relaxation for evolution inclusions of the subdifferential type
In this paper we consider parametric nonlinear evolution inclusions driven by time-dependent subdifferentials. First we prove some continuous dependence results for the solution set (of both the convex and nonconvex problems) and for the set of solution-selector pairs (of the convex problem). Then we derive a continuous version of the “Filippov-Gronwall” inequality and using it, we prove the parametric relaxation theorem. An example of a parabolic distributed parameter system is also worked out...
A strong relaxation theorem for maximal monotone differential inclusions with memory
We consider maximal monotone differential inclusions with memory. We establish the existence of extremal strong and then we show that they are dense in the solution set of the original equation. As an application, we derive a “bang-bang” principle for nonlinear control systems monitored by maximal monotone differential equations.
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.
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