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We consider the equation $- y^{'} (x) + q (x) y (x - ϕ (x)) = f (x), x \in ℝ,$ where $ϕ$ and $q$ ( $q \geq 1$ ) are positive continuous functions for all $x \in ℝ$ and $f \in C (ℝ)$ . By a solution of the equation we mean any function $y$ , continuously differentiable everywhere in $ℝ$ , which satisfies the equation for all $x \in ℝ$ . We show that under certain additional conditions on the functions $ϕ$ and $q$ , the above equation has a unique solution $y$ , satisfying the inequality $∥ y^{'} ∥_{C (ℝ)} + {∥ q y ∥}_{C (ℝ)} \leq c {∥ f ∥}_{C (ℝ)},$ where the constant $c \in (0, \infty)$ does not depend on the choice of $f$ .

Algebraic elements in the transformation theory of 2nd order linear oscillatory differential equations

Borůvka, O. (1967)

Differential Equations and Their Applications

Algebraic properties of phases of the differential equation $y^{'} = q (t) y$

Irena Rachůnková (1978)

Sborník prací Přírodovědecké fakulty University Palackého v Olomouci. Matematika

Algebraic solutions of the Lamé equation

Frits Beukers (2002)

Banach Center Publications

In this paper we give a summary of joint work with Alexa van der Waall concerning Lamé equations having finite monodromy. This research is the subject of van der Waall's Ph. D. thesis [W].

Algebraische Theorie der Transformation der linearen Differentialgleichungen

Zdeněk Hustý (1975)

Czechoslovak Mathematical Journal

Almost Floquet and generalized almost Floquet systems

Herbert I. Freedman, John J. Mallet-Paret (1976)

Czechoslovak Mathematical Journal

Amplitudes of linear oscillations determined by linear homogenous differential equation of the second order and Liouville-Besge formulae

Miloje Rajović, Dragan Dimitrovski (2011)

Kragujevac Journal of Mathematics

An abstract model of linear differential transformations

Erich Barvínek (1975)

Archivum Mathematicum

An algorithm for determining the number of linearly independent comitants of a system of differential equations

Н.И. Вулпе, К.С. Чеботарь (1982)

Matematiceskie issledovanija

An almost-periodicity criterion for solutions of the oscillatory differential equation $y^{''} = q (t) y$ and its applications

Staněk, Svatoslav (2005)

Archivum Mathematicum

The linear differential equation $(q) : y^{''} = q (t) y$ with the uniformly almost-periodic function $q$ is considered. Necessary and sufficient conditions which guarantee that all bounded (on $ℝ$ ) solutions of $(q)$ are uniformly almost-periodic functions are presented. The conditions are stated by a phase of $(q)$ . Next, a class of equations of the type $(q)$ whose all non-trivial solutions are bounded and not uniformly almost-periodic is given. Finally, uniformly almost-periodic solutions of the non-homogeneous differential equations...

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About one inverse problem in the theory of linear differential equations with measures as coefficients

About The Fundamental Matrix Of The Linear Nonstationary System

Accompanying spaces to a linear two-dimensional space of continuous functions with a continuous first derivative

Addition à un mémoire sur les équations différentielles linéaires

Addition theorems for solutions to linear homogeneous constant coefficient ordinary differential equations. (Short Communication).

Addition theorems for solutions to linear homogeneous constant coefficient ordinary differential equations.

Adjoint operators and boundary value problems for linear differential equations

Admissible spaces for a first order differential equation with delayed argument