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On periodic oscillations for a class of feedback control systems in Hilbert spaces

Nguyen Van Loi (2013)

Discussiones Mathematicae, Differential Inclusions, Control and Optimization

In this paper, by using the topological degree theory for multivalued maps and the method of guiding functions in Hilbert spaces we deal with the existence of periodic oscillations for a class of feedback control systems in Hilbert spaces.

On periodic solutions of non-autonomous second order Hamiltonian systems

Xingyong Zhang, Yinggao Zhou (2010)

Applications of Mathematics

The purpose of this paper is to study the existence of periodic solutions for the non-autonomous second order Hamiltonian system u ¨ ( t ) = F ( t , u ( t ) ) , a.e. t [ 0 , T ] , u ( 0 ) - u ( T ) = u ˙ ( 0 ) - u ˙ ( T ) = 0 . Some new existence theorems are obtained by the least action principle.

On periodic solutions of systems of linear functional-differential equations

Ivan Kiguradze, Bedřich Půža (1997)

Archivum Mathematicum

This paper deals with the system of functional-differential equations d x ( t ) d t = p ( x ) ( t ) + q ( t ) , where p : C ω ( R n ) L ω ( R n ) is a linear bounded operator, q L ω ( R n ) , ω > 0 and C ω ( R n ) and L ω ( R n ) are spaces of n -dimensional ω -periodic vector functions with continuous and integrable on [ 0 , ω ] components, respectively. Conditions which guarantee the existence of a unique ω -periodic solution and continuous dependence of that solution on the right hand side of the system considered are established.

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