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Asymptotic estimates of solutions and their derivatives for n-th order nonhomogeneous ODEs with constant coefficients are obtained, provided the associated characteristic polynomial is (asymptotically) stable. Assuming, additionally, the stability of the so called "shifted polynomials" (see below) to the characteristic one, the estimates can be still improved.

Asymptotic estimation for functional differential equations with several delays

Jan Čermák (1999)

Archivum Mathematicum

We discuss the asymptotic behaviour of all solutions of the functional differential equation $y^{'} (x) = \sum_{i = 1}^{m} a_{i} (x) y (τ_{i} (x)) + b (x) y (x),$ where $b (x) < 0$ . The asymptotic bounds are given in terms of a solution of the functional nondifferential equation $\sum_{i = 1}^{m} | a_{i} (x) | ω (τ_{i} (x)) + b (x) ω (x) = 0 .$

Asymptotic estimation of the convergence of solutions of the equation $\dot{x} (t) = b (t) x (t - τ (t))$

Josef Diblík, Denis Khusainov (2001)

Archivum Mathematicum

The main result of the present paper is obtaining new inequalities for solutions of scalar equation $\dot{x} (t) = b (t) x (t - τ (t))$ . Except this the interval of transient process is computed, i.e. the time is estimated, during which the given solution $x (t)$ reaches an $ε$ - neighbourhood of origin and remains in it.

Asymptotic expansion formulas for the maximum of solutions to diffusive logistic equations.

Shibata, Tetsutaro (2008)

Electronic Journal of Differential Equations (EJDE) [electronic only]

Asymptotic expansions of canards with poles. Application to the stationary unidimensional Schrödinger equation.

Benoit, E. (1996)

Bulletin of the Belgian Mathematical Society - Simon Stevin

Asymptotic expansions of integral functionals of weakly correlated random processes.

vom Scheidt, J., Starkloff, H.-J., Wunderlich, R. (2000)

Zeitschrift für Analysis und ihre Anwendungen

Asymptotic expansions of quasiperiodic solutions

L. Chierchia, E. Zehnder (1989)

Annali della Scuola Normale Superiore di Pisa - Classe di Scienze

Asymptotic expansions of solutions of the equation ${(p (x) y^{'})}^{'} - q (x) y = 0$ with complex-valued coefficients

Miloš Ráb (1972)

Archivum Mathematicum

Asymptotic expansions of solutions to the fifth Painlevé equation in neighbourhoods of singular and nonsingular points of the equation

Anastasia Parusnikova (2012)

Banach Center Publications

Applying methods of plane Power Geometry we are looking for the asymptotic expansions of solutions to the fifth Painlevé equation in the neighbourhood of its singular and nonsingular points.

Asymptotic Expansions of the Global Error of Fixed-Stepsize Methods.

E. Hairer, C. Lubich (1984)

Numerische Mathematik

Asymptotic forms of solutions of perturbed half-linear ordinary differential equations

Sokea Luey, Hiroyuki Usami (2021)

Archivum Mathematicum

Asymptotic forms of solutions of half-linear ordinary differential equation $(| u^{'} |^{α - 1} u^{'})^{'} = α (1 + b (t)) {| u |}^{α - 1} u$ are investigated under a smallness condition and some signum conditions on $b (t)$ . When $α = 1$ , our results reduce to well-known ones for linear ordinary differential equations.

Asymptotic formulas for solutions of the differential equation with advanced argument ${(x^{'} (t) / r (t))}^{'} + q (t) f (x (g (t))) = 0$

Miloš Ráb (1987)

Archivum Mathematicum

Asymptotic formulas for solutions of the equation ${[p (t) y^{'}]}^{'} = q (t) y + r (t)$

Miloš Ráb (1974)

Archivum Mathematicum

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Asymptotic equivalence of impulsive differential equations in a Banach space.

Asymptotic equivalence of second order differential equations

Asymptotic Error Expansions for Stiff Equations: an Analysis for the Implicit Midpoint and Trapezoidal Rules in the Strongly Stiff Case.

Asymptotic estimates for the growth of meromorphic solutions to differential equations in angular domains.

Asymptotic estimates of solutions and their derivatives for n-th order nonhomogeneous ordinary differential equations with constant coefficients

Asymptotic estimation for functional differential equations with several delays

Asymptotic estimation of the convergence of solutions of the equation $\dot{x} (t) = b (t) x (t - τ (t))$

Asymptotic expansion formulas for the maximum of solutions to diffusive logistic equations.

Asymptotic expansions of canards with poles. Application to the stationary unidimensional Schrödinger equation.

Asymptotic expansions of integral functionals of weakly correlated random processes.

Asymptotic expansions of quasiperiodic solutions

Asymptotic expansions of solutions of the equation ${(p (x) y^{'})}^{'} - q (x) y = 0$ with complex-valued coefficients

Asymptotic expansions of solutions to the fifth Painlevé equation in neighbourhoods of singular and nonsingular points of the equation

Asymptotic Expansions of the Global Error of Fixed-Stepsize Methods.

Asymptotic forms of solutions of perturbed half-linear ordinary differential equations

Asymptotic forms of weakly increasing positive solutions for quasilinear ordinary differential equations.

Asymptotic formulas and critical exponents for two-parameter nonlinear eigenvalue problems.

Asymptotic formulas for solutions of functional-differential equations

Asymptotic formulas for solutions of the differential equation with advanced argument ${(x^{'} (t) / r (t))}^{'} + q (t) f (x (g (t))) = 0$

Asymptotic formulas for solutions of the equation ${[p (t) y^{'}]}^{'} = q (t) y + r (t)$

Currently displaying 1101 – 1120 of 9312