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On the existence of one-signed periodic solutions of some differential equations of second order

Jan Ligęza (2006)

Acta Universitatis Palackianae Olomucensis. Facultas Rerum Naturalium. Mathematica

We study the existence of one-signed periodic solutions of the equations x ' ' ( t ) - a 2 ( t ) x ( t ) + μ f ( t , x ( t ) , x ' ( t ) ) = 0 , x ' ' ( t ) + a 2 ( t ) x ( t ) = μ f ( t , x ( t ) , x ' ( t ) ) , where μ > 0 , a : ( - , + ) ( 0 , ) is continuous and 1-periodic, f is a continuous and 1-periodic in the first variable and may take values of different signs. The Krasnosielski fixed point theorem on cone is used.

On the existence of optimal controls for nonlinear infinite dimensional systems

Antonella Fiacca, Nikolaos S. Papageorgiou, Francesca 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.

On the solutions of the inhomogeneous evolution equation in Banach spaces

Eugenio Sinestrari (1981)

Atti della Accademia Nazionale dei Lincei. Classe di Scienze Fisiche, Matematiche e Naturali. Rendiconti Lincei. Matematica e Applicazioni

Vengono dati nuovi teoremi di regolarità per le soluzioni dell'equazione u ( t ) = Λ u ( t ) + f ( t ) nel caso in cui Λ è il generatore infinitesimale di un semigruppo analitico in uno spazio di Banach E e f è una funzione continua.

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