Displaying similar documents to “On periodic-type solutions of systems of linear ordinary differential equations.”

On periodic solutions of systems of linear functional-differential equations

Ivan Kiguradze, Bedřich Půža (1997)

Archivum Mathematicum

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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.

On periodic in the plane solutions of second order linear hyperbolic systems

Tariel Kiguradze (1997)

Archivum Mathematicum

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Sufficient conditions for the problem ∂ 2 u ∂ x ∂ y = P 0 ( x , y ) u + P 1 ( x , y ) ∂ u ∂ x + P 2 ( x , y ) ∂ u ∂ y + q ( x , y ) , u ( x + ω 1 , y ) = u ( x , y ) , u ( x , y + ω 2 ) = u ( x , y ) to have the Fredholm property and to be uniquely solvable are established, where ω 1 and ω 2 are positive constants and P j : R 2 → R n × n ( j = 0 , 1 , 2 ) and q : R 2 → R n are continuous matrix and vector functions periodic in x and y .