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New optimal conditions for unique solvability of the Cauchy problem for first order linear functional differential equations

Robert Hakl, Alexander Lomtatidze, Bedřich Půža (2002)

Mathematica Bohemica

The nonimprovable sufficient conditions for the unique solvability of the problem u ' ( t ) = ℓ ( u ) ( t ) + q ( t ) , u ( a ) = c , where ℓ C ( I ; ℝ ) → L ( I ; ℝ ) is a linear bounded operator, q ∈ L ( I ; ℝ ) , c ∈ ℝ , are established which are different from the previous results. More precisely, they are interesting especially in the case where the operator ℓ is not of Volterra’s type with respect to the point a .

Note on simultaneous solutions of a system of Schröder's equations

Jan Čermák (1995)

Mathematica Bohemica

We investigate simultaneous solutions of a system of Schroder's functional equations. Under certain assumptions these solutions are used in transformations of functional-differential equations the initial set of which consists of the initial point only.

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