Displaying similar documents to “On an antiperiodic type boundary value problem for first order linear functional differential equations”

On solvability of nonlinear boundary value problems for the equation ( x ' + g ( t , x , x ' ) ) ' = f ( t , x , x ' ) with one-sided growth restrictions on f

Staněk, Svatoslav (2002)

Archivum Mathematicum

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We consider boundary value problems for second order differential equations of the form ( x ' + g ( t , x , x ' ) ) ' = f ( t , x , x ' ) with the boundary conditions r ( x ( 0 ) , x ' ( 0 ) , x ( T ) ) + ϕ ( x ) = 0 , w ( x ( 0 ) , x ( T ) , x ' ( T ) ) + ψ ( x ) = 0 , where g , r , w are continuous functions, f satisfies the local Carathéodory conditions and ϕ , ψ are continuous and nondecreasing functionals. Existence results are proved by the method of lower and upper functions and applying the degree theory for α -condensing operators.

A note on the Cauchy problem for first order linear differential equations with a deviating argument

Robert Hakl, Alexander Lomtatidze (2002)

Archivum Mathematicum

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Conditions for the existence and uniqueness of a solution of the Cauchy problem u ' ( t ) = p ( t ) u ( τ ( t ) ) + q ( t ) , u ( a ) = c , established in [2], are formulated more precisely and refined for the special case, where the function τ maps the interval ] a , b [ into some subinterval [ τ 0 , τ 1 ] ⊆ [ a , b ] , which can be degenerated to a point.