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This contribution is devoted to the problem of asymptotic behaviour of solutions of scalar linear differential equation with variable bounded delay of the form $\dot{x} (t) = - c (t) x (t - τ (t)) (^{*})$ with positive function $c (t) .$ Results concerning the structure of its solutions are obtained with the aid of properties of solutions of auxiliary homogeneous equation $\dot{y} (t) = β (t) [y (t) - y (t - τ (t))]$ where the function $β (t)$ is positive. A result concerning the behaviour of solutions of Eq. (*) in critical case is given and, moreover, an analogy with behaviour of solutions of...

Behaviour of solutions to the Dirichlet problem for the biharmonic operator at a boundary point

Maz'ya, V. G. (1979)

Equadiff IV

Bemerkung über die Form der Integrale der linearen Differentialgleichungen mit veränderlichen Coefficienten.

H.L. Hamburger (1873)

Journal für die reine und angewandte Mathematik

Bemerkung zu einem Vergleichssatz für gewöhnliche lineare Differentialgleichungen.

Albert Schneider (1972)

Manuscripta mathematica

Bemerkung zum Tschaplyginschen Satz über Differentialungleichungen

Staněk, Svatoslav (1972)

Acta Universitatis Palackianae Olomucensis. Facultas Rerum Naturalium. Mathematica-Physica-Chemica

Bemerkungen zu Stabilitätsfragen für verallgemeinerte Differentialgleichungen

Štefan Schwabik (1971)

Časopis pro pěstování matematiky

Berechnung des charakteristischen Exponenten der endlichen Hillschen Differentialgleichung durch Numerische Integration.

E. Wagenführer, H. Lang (1979)

Numerische Mathematik

Bergman spaces on some tube-type domains and Laguerre operators on symmetric cones.

Fulvio Ricci, Anita Tabacco Vignati (1994)

Journal für die reine und angewandte Mathematik

Bernstein classes

N. Roytwarf, Yosef Yomdin (1997)

Annales de l'institut Fourier

One of the classical Bernstein inequalities compares the maxima of a polynomial of a given degree on the interval [-1,1] and on the ellipse in the complex plane with the focuses -1, 1 and the semiaxes $R$ . We prove a similar inequality for a branch of an algebraic function of a given degree on the maximal disk of its regularity, with the explicitly given constant, depending on the degree only. In particular, this improves a recent inequality of Fefferman and Narasimhan and answers one of their questions....

Bernstein polynomials and spectral numbers for linear free divisors

Christian Sevenheck (2011)

Annales de l’institut Fourier

We discuss Bernstein polynomials of reductive linear free divisors. We define suitable Brieskorn lattices for these non-isolated singularities, and show the analogue of Malgrange’s result relating the roots of the Bernstein polynomial to the residue eigenvalues on the saturation of these Brieskorn lattices.

Bessel matrix differential equations: explicit solutions of initial and two-point boundary value problems

Enrique Navarro, Rafael Company, Lucas Jódar (1993)

Applicationes Mathematicae

In this paper we consider Bessel equations of the type $t^{2} X^{(2)} (t) + t X^{(1)} (t) + (t^{2} I - A^{2}) X (t) = 0$ , where A is an n $\times$ n complex matrix and X(t) is an n $\times$ m matrix for t > 0. Following the ideas of the scalar case we introduce the concept of a fundamental set of solutions for the above equation expressed in terms of the data dimension. This concept allows us to give an explicit closed form solution of initial and two-point boundary value problems related to the Bessel equation.

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Behavior of forced asymmetric oscillators at resonance.

Behavior of positive radial solutions of a quasilinear equation with a weighted Laplacian.

Behavior of second order nonlinear differential equations.

Behavior of the solutions to second order linear autonomous delay differential equations.

Behaviour of solutions of a fourth-order self-adjoint linear differential equation

Behaviour of solutions of linear differential equations with delay