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1
Content available remote

Asymptotic behaviour of solutions of linear differential equations with delay

100%
Diblík J.
Annales Polonici Mathematici
|
1993
|
tom 58
|
nr 2
131-137
EN
Inequalities for some positive solutions of the linear differential equation with delay ẋ(t) = -c(t)x(t-τ) are obtained. A connection with an auxiliary functional nondifferential equation is used.
2
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Oscillation criteria for a class of nonlinear differential equations of third order

80%
Parhi N., Das P.
Annales Polonici Mathematici
|
1992
|
tom 57
|
nr 3
219-229
EN
Oscillation criteria are obtained for nonlinear homogeneous third order differential equations of the form $y''' + q(t)y' + p(t)y^α = 0$ and y''' + q(t)y' + p(t)f(y) = 0, where p and q are real-valued continuous functions on [a,∞), f is a real-valued continuous function on (-∞, ∞) and α > 0 is a quotient of odd integers. Sign restrictions are imposed on p(t) and q(t). These results generalize some of the results obtained earlier in this direction.
3
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Oscillatory behaviour of solutions of forced neutral differential equations

80%
Parhi N., Mohanty P.
Annales Polonici Mathematici
|
1996-1997
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tom 65
|
nr 1
1-10
EN
Sufficient conditions are obtained for oscillation of all solutions of a class of forced nth order linear and nonlinear neutral delay differential equations. Also, asymptotic behaviour of nonoscillatory solutions of a class of forced first order neutral equations is studied.
4
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On the delay differential equation y'(x) = ay(τ(x)) + by(x)

80%
Čermák J.
Annales Polonici Mathematici
|
1999
|
tom 71
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nr 2
161-169
EN
The paper discusses the asymptotic properties of solutions of the scalar functional differential equation $y'(x) = ay(τ(x)) + by(x), x ∈ [x_0,∞]$. Asymptotic formulas are given in terms of solutions of the appropriate scalar functional nondifferential equation.
5
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Asymptotic behaviour of a discrete dynamical system generated by a simple evolutionary process

70%
Karcz-Dulęba I.
International Journal of Applied Mathematics and Computer Science
|
2004
|
tom 14
|
nr 1
79-90
EN
A simple model of phenotypic evolution is introduced and analysed in a space of population states. The expected values of the population states generate a discrete dynamical system. The asymptotic behaviour of the system is studied with the use of classical tools of dynamical systems. The number, location and stability of fixed points of the system depend on parameters of a fitness function and the parameters of the evolutionary process itself. The influence of evolutionary process parameters on the stability of the fixed points is discussed. For large values of the standard deviation of mutation, fixed points become unstable and periodical orbits arise. An analysis of the periodical orbits is presented.
6
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A note on convergence of semigroups

61%
Bobrowski A.
Annales Polonici Mathematici
|
1998
|
tom 69
|
nr 2
107-127
EN
Convergence of semigroups which do not converge in the Trotter-Kato-Neveu sense is considered.
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