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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 $f$ .

Affinity integral manifolds for impulsive differential equations.

Kostadinov, S.I., Stamov, G.T. (1999)

Zeitschrift für Analysis und ihre Anwendungen

Affinor structures in the oscillation theory

Boris N. Shapukov (2002)

Banach Center Publications

In this paper we consider the system of Hamiltonian differential equations, which determines small oscillations of a dynamical system with n parameters. We demonstrate that this system determines an affinor structure J on the phase space TRⁿ. If J² = ωI, where ω = ±1,0, the phase space can be considered as the biplanar space of elliptic, hyperbolic or parabolic type. In the Euclidean case (Rⁿ = Eⁿ) we obtain the Hopf bundle and its analogs. The bases of these bundles are, respectively, the projective...

Algebraic curve solution for second-order polynomial autonomous systems.

Zhaosheng, Feng (2001)

ELA. The Electronic Journal of Linear Algebra [electronic only]

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

Borůvka, O. (1967)

Differential Equations and Their Applications

Algebraic integrability for minimum energy curves

Ivan Yudin, Fátima Silva Leite (2015)

Kybernetika

This paper deals with integrability issues of the Euler-Lagrange equations associated to a variational problem, where the energy function depends on acceleration and drag. Although the motivation came from applications to path planning of underwater robot manipulators, the approach is rather theoretical and the main difficulties result from the fact that the power needed to push an object through a fluid increases as the cube of its speed.

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].