On nonnegative solutions of a certain boundary value problem for first order linear functional differential equations.

Nonimprovable, in a sense sufficient conditions guaranteeing the unique solvability of the problem $u^{'} (t) = ℓ (u) (t) + q (t), u (a) = c,$ where $ℓ C (I, ℝ) \to L (I, ℝ)$ is a linear bounded operator, $q \in L (I, ℝ)$ , and $c \in ℝ$ , are established.

Integral equations, Volterra equations, and the remarkable resolvent: contractions.

Burton, T.A. (2006)

Electronic Journal of Qualitative Theory of Differential Equations [electronic only]

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Positive solutions of Volterra integro-differential equations.

Wu, Yumei (1995)

Acta Mathematica Universitatis Comenianae. New Series

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A Liapunov functional for a linear integral equation.

Burton, T.A. (2010)

Electronic Journal of Qualitative Theory of Differential Equations [electronic only]

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Solvability conditions of the Cauchy problem for two-dimensional systems of linear functional differential equations with monotone operators

Jiří Šremr (2007)

Mathematica Bohemica

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We establish new efficient conditions sufficient for the unique solvability of the initial value problem for two-dimensional systems of linear functional differential equations with monotone operators.