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Extremal solutions for nonlinear neumann problems

Antonella FiaccaRaffaella Servadei — 2001

Discussiones Mathematicae, Differential Inclusions, Control and Optimization

In this paper, we study a nonlinear Neumann problem. Assuming the existence of an upper and a lower solution, we prove the existence of a least and a greatest solution between them. Our approach uses the theory of operators of monotone type together with truncation and penalization techniques.

On the existence of optimal controls for nonlinear infinite dimensional systems

Antonella FiaccaNikolaos S. PapageorgiouFrancesca Papalini — 1998

Czechoslovak Mathematical Journal

We consider nonlinear systems with a priori feedback. We establish the existence of admissible pairs and then we show that the Lagrange optimal control problem admits an optimal pair. As application we work out in detail two examples of optimal control problems for nonlinear parabolic partial differential equations.

Nonlinear elliptic differential equations with multivalued nonlinearities

Antonella FiaccaNikolaos M. MatzakosNikolaos S. PapageorgiouRaffaella Servadei — 2003

Czechoslovak Mathematical Journal

In this paper we study nonlinear elliptic boundary value problems with monotone and nonmonotone multivalued nonlinearities. First we consider the case of monotone nonlinearities. In the first result we assume that the multivalued nonlinearity is defined on all . Assuming the existence of an upper and of a lower solution, we prove the existence of a solution between them. Also for a special version of the problem, we prove the existence of extremal solutions in the order interval formed by the upper...

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