Displaying similar documents to “An optimal condition for the uniqueness of a periodic solution for linear functional differential systems.”

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

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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 an antiperiodic type boundary value problem for first order linear functional differential equations

Robert Hakl, Alexander Lomtatidze, Jiří Šremr (2002)

Archivum Mathematicum

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Nonimprovable, in a certain sense, sufficient conditions for the unique solvability of the boundary value problem u ' ( t ) = ℓ ( u ) ( t ) + q ( t ) , u ( a ) + λ u ( b ) = c are established, where ℓ : C ( [ a , b ] ; R ) → L ( [ a , b ] ; R ) is a linear bounded operator, q ∈ L ( [ a , b ] ; R ) , λ ∈ R + , and c ∈ R . The question on the dimension of the solution space of the homogeneous problem u ' ( t ) = ℓ ( u ) ( t ) , u ( a ) + λ u ( b ) = 0 is discussed as well.