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Start Over Subject differential equation

1. Asymptotic behaviour of solutions of some linear delay differential equations.

Creator:
Čermák, Jan
Format:
bez média and svazek
Type:
model:article and TEXT
Subject:
asymptotic behaviour, differential equation, delayed argument, and functional equation
Language:
English
Description:
In this paper we investigate the asymptotic properties of all solutions of the delay differential equation y'(x)=a(x)y(\tau(x))+b(x)y(x),\qquad x\in I=[x_0,\infty). We set up conditions under which every solution of this equation can be represented in terms of a solution of the differential equation z'(x)=b(x)z(x),\qquad x\in I and a solution of the functional equation |a(x)|\varphi(\tau(x))=|b(x)|\varphi(x),\qquad x\in I.
Rights:
http://creativecommons.org/publicdomain/mark/1.0/ and policy:public

2. Coordinate description of analytic relations

Creator:
Neuman, František
Format:
bez média and svazek
Type:
model:article and TEXT
Subject:
canonical form, Brandt groupoid, Ehresmann groupoid, transformation, differential equation, Abel functional equation, and functional differential equation
Language:
English
Description:
In this paper we present an algebraic approach that describes the structure of analytic objects in a unified manner in the case when their transformations satisfy certain conditions of categorical character. We demonstrate this approach on examples of functional, differential, and functional differential equations.
Rights:
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3. Differential equations in metric spaces

Creator:
Tabor, Jacek
Format:
bez média and svazek
Type:
model:article and TEXT
Subject:
differential equation and tangent space
Language:
English
Description:
We give a meaning to derivative of a function u: R → X, where X is a complete metric space. This enables us to investigate differential equations in a metric space. One can prove in particular Gronwall’s Lemma, Peano and Picard Existence Theorems, Lyapunov Theorem or Nagumo Theorem in metric spaces. The main idea is to define the tangent space TxX of x ∈ X. Let u, v : [0, 1) → X, u(0) = v(0) be continuous at zero. Then by the definition u and v are in the same equivalence class if they are tangent at zero, that is if lim h→0+ d(u(h), v(h)) ⁄ h = 0. By TxX we denote the set of all equivalence classes of continuous at zero functions u: [0, 1) → X, u(0) = x, and by T X the disjoint sum of all TxX over x ∈ X. By u (t) ∈ Tu(t)X, where u: → X, we understand the equivalence class of a function [0, 1) h → u(t + h) ∈ X. Given a function F : X → T X such that F(x) ∈ TxX we are now able to investigate solutions to the differential equation u (t) = F(u(t)).
Rights:
http://creativecommons.org/publicdomain/mark/1.0/ and policy:public

4. Kermack-McKendrick epidemics vaccinated

Creator:
Staněk, Jakub
Format:
bez média and svazek
Type:
model:article and TEXT
Subject:
SIR epidemic models, vaccination, and differential equation
Language:
English
Description:
This paper proposes a deterministic model for the spread of an epidemic. We extend the classical Kermack-McKendrick model, so that a more general contact rate is chosen and a vaccination added. The model is governed by a differential equation (DE) for the time dynamics of the susceptibles, infectives and removals subpopulation. We present some conditions on the existence and uniqueness of a solution to the nonlinear DE. The existence of limits and uniqueness of maximum of infected individuals are also discussed. In the final part, simulations, numerical results and comparisons of the different vaccination strategies are presented.
Rights:
http://creativecommons.org/publicdomain/mark/1.0/ and policy:public

5. Mathematical model for vibrations of non-uniform flexural beams

Creator:
Taha, Mohamed Hussien and Abohadima, Samir
Format:
bez média and svazek
Type:
model:article and TEXT
Subject:
damped vibration, non-uniform beam, differential equation, variable coefficients, series solution, and mode shapes and natural frequencies
Language:
English
Description:
A simplified mathematical model for free vibrations of nonuniform viscoelastic flexural beams is presented. The mass intensity, the material damping intensity and the flexural stiffness of the beam are assumed varying as power functions along the beam. An analytical solution for the fourth order differential equations of beam vibration under appropriate boundary conditions is obtained by factorization. Mode shapes and damped natural frequencies of the beam are obtained for wide range of beam characteristics. The model results agree with those found in literature for uniform beams. and Obsahuje seznam literatury
Rights:
http://creativecommons.org/licenses/by-nc-sa/4.0/ and policy:public

6. N-widths for singularly perturbed problems

Creator:
Stynes, Martin and Kellogg, R. Bruce
Format:
bez média and svazek
Type:
model:article and TEXT
Subject:
N-width, singularly perturbed, differential equation, boundary value problem, convection-diffusion, and reaction-diffusion
Language:
English
Description:
Kolmogorov N-widths are an approximation theory concept that, for a given problem, yields information about the optimal rate of convergence attainable by any numerical method applied to that problem. We survey sharp bounds recently obtained for the N-widths of certain singularly perturbed convection-diffusion and reaction-diffusion boundary value problems.
Rights:
http://creativecommons.org/publicdomain/mark/1.0/ and policy:public

7. Oscillation of second order neutral delay differential equations

Creator:
Džurina, J. and Hudáková, D.
Format:
bez média and svazek
Type:
model:article and TEXT
Subject:
differential equation, oscillation, second order, delay, neutral type, and integral averaging method
Language:
English
Description:
We establish some new oscillation criteria for the second order neutral delay differential equation [r(t)|[x(t) + p(t)x[τ (t)]]′ | α−1 [x(t) + p(t)x[τ (t)]]′ ] ′ + q(t)f(x[σ(t)]) = 0. The obtained results supplement those of Dzurina and Stavroulakis, Sun and Meng, Xu and Meng, Baculíková and Lacková. We also make a slight improvement of one assumption in the paper of Xu and Meng.
Rights:
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8. Oscillatory behaviour of a higher order nonlinear neutral delay type functional differential equation with oscillating coefficients

Creator:
Bolat, Yasar and Akin, Ömer
Format:
bez média and svazek
Type:
model:article and TEXT
Subject:
differential equation, higher order nonlinear neutral differential equation, oscillation, and oscillating coefficients
Language:
English
Description:
In this paper we are concerned with the oscillation of solutions of a certain more general higher order nonlinear neutral type functional differential equation with oscillating coefficients. We obtain two sufficient criteria for oscillatory behaviour of its solutions.
Rights:
http://creativecommons.org/publicdomain/mark/1.0/ and policy:public