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1
Content available Existence and asymptotic behavior of nonoscillatory solutions of half-linear ordinary differential equations
Naito Manabu
Opuscula Mathematica
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2023
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Vol. 43, no. 2
221--246
EN
We consider the half-linear differential equation (|x′|αsgn x′)′ + q(t)|x|αsgn x = 0, t ≥ t0, under the condition [formula] It is shown that if certain additional conditions are satisfied, then the above equation has a pair of nonoscillatory solutions with specific asymptotic behavior as t → ∞.
2
Content available Remarks on the existence of nonoscillatory solutions of half-linear ordinary differential equations, I
Naito Manabu
Opuscula Mathematica
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2021
|
Vol. 41, no. 1
71--94
EN
We consider the half-linear differential equation of the form [formula], under the assumption [formula]. It is shown that if a certain condition is satisfied, then the above equation has a pair of nonoscillatory solutions with specific asymptotic behavior as t →∞.
3
Content available Oscillations of equations caused by several deviating arguments
Chatzarakis George E
Opuscula Mathematica
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2019
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Vol. 39, no. 3
321--353
EN
Linear delay or advanced differential equations with variable coefficients and several not necessarily monotone arguments are considered, and some new oscillation criteria are given. More precisely, sufficient conditions, involving limsup and liminf, are obtained, which essentially improve several known criteria existing in the literature. Examples illustrating the results are also given, numerically solved in MATLAB.
4
Content available Improved iterative oscillation tests for first-order deviating differential equations
Chatzarakis G. E, Jadlovska I.
Opuscula Mathematica
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2018
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Vol. 38, no. 3
327--356
EN
In this paper, improved oscillation conditions are established for the oscillation of all solutions of differential equations with non-monotone deviating arguments and nonnegative coefficients. They lead to a procedure that checks for oscillations by iteratively computing lim sup and lim inf on terms recursively defined on the equation's coefficients and deviating argument. This procedure significantly improves all known oscillation criteria. The results and the improvement achieved over the other known conditions are illustrated by two examples, numerically solved in MATLAB.
5
Content available remote On asymptotic property of solutions of higher order functional differential equations
Padhi S., Qian C.
Fasciculi Mathematici
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2011
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Nr 46
87--104
EN
We establish sucient conditions for the linear func- tional differential equation of n-th order of the forms y(n)(t) + p(t)y(g(t)) = 0 and y(n)(t) - p(t)y(g(t)) = 0 to have property A and B, where p and g ϵ C ([σ, ∞), (0, ∞)), with g ϵ R and g(t) ≥ t, and n ≥ 2 is a positive integer
6
Content available remote Oscillation and non-oscillation criteria for a neutral delay difference equation of first order
Rath R., Rath S. K.
Fasciculi Mathematici
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2009
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Nr 42
109-120
EN
In this paper, necessary and sufficient condition are obtained so that every bounded solution of Δ(yn - yn-k) + qnG(yσ(n)) = 0 is oscillatory, under a condition weaker than ...[wzór]
7
Content available remote Oscillation and asymptotic behaviour of solutions of second order neutral differential equations with positive and negative coefficients
Padhi S.
Fasciculi Mathematici
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2007
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Nr 38
105-114
EN
Sufficient conditions in terms of the coefficient functions for the oscillation and asymptotic behavior of nonoscillatory solutions of a class of second order nonlinear neutral differential equations have been obtained. The results improve some earlier results.
8
Content available Oscillatory properties of fourth order nonlinear difference equations with quasidifferences
Schmeidel E., Migda M., Musielak A.
Opuscula Mathematica
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2006
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Vol. 26, no. 2
371-380
EN
In this paper we present the oscillation criterion for a class of fourth order nonlinear difference equations with quasidifferences.
9
Content available Asymptotic properties of nonoscillatory solutions of higher order neutral difference equations
Migda M.
Opuscula Mathematica
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2006
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Vol. 26, no. 3
507-514
EN
In this paper we study asymptotic behavior of solutions of a higher order neutral difference equation of the form Δm(xn + pnxn-τ) + f(n, xσ(n)) = hn. We present conditions under which all nonoscillatory solutions of the above equation have the property xn = cnm-1 + o(nm-1) for some c ∈ R.
10
Content available remote On the discrete version of generalized Kiguradze's lemma
Migda M.
Fasciculi Mathematici
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2005
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Nr 35
77-83
EN
The Kiguaradze's lemma for quasi-differeuces of a real sequence is presented. Some examples illustrating the result are included.
11
Content available remote Oscillatory and asymptotic behavior of fourth order nonlinear delay difference equations
Graef J. R., Thandapani E.
Fasciculi Mathematici
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2001
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Nr 31
23-36
EN
The authors consider the nonlinear difference equation (E) delta2 ((delta(bn delta yn))+f(n,yn-t)=0, n należy N(no)={no,no+1,...}, here {an} and {bn} are positive real sequences, I is a nonnegative integer, f: N(no) x R R is a continuous function with uf(n, u) > 0 for all u nierówne 0. They obtain necessary and sufficient conditions for the existence of nonoscillatory solutions with a specified asymptotic behavior. They also obtain sufficient conditions for all solutions to be oscillatory if/ is either strongly sublinear or strongly superlinear. Examples of their results are also included.
12
Content available remote Existence of nonoscillatory solutions of the third order quasilinear neutral differential equations
Janik V., Marusiak P.
Fasciculi Mathematici
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2001
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Nr 31
45-55
EN
In the paper there are given sufficient and necessary conditions for the existence of nonoscillatory solutions of the equation (r2 (t)(r1(t)$(Lox(t000`)`t,x(g(t,x(g(t)))=0 with specified asymptotic behaviour as t -ť oo.
13
Content available remote Asymptotic behavior of solutions of second order neutral difference equations with "maxima"
Luo J., Yu Y.
Demonstratio Mathematica
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2001
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Vol. 34, nr 1
83-89
EN
Second order neutral difference equations with "maxima" are considered and some asymptotic properties of nonoscillatory solutions are given.
14
Content available remote Comparison theorems for n-th order nonlinear differential inequalities with deviating argument
Seman J.
Fasciculi Mathematici
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1999
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Nr 29
113-124
EN
This paper deals with comparison theorems for oscillatorineess all solutions of the n-th order nonlinear differential inequalities with quasiderivativer and deviatimg argument of a form [formula]
15
Content available remote Oscillations of some difference equations
Szafrański Z., Szmanda B.
Fasciculi Mathematici
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1998
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Nr 28
149-155
EN
Oscillation criteria for nonlinear difference equation ofthe fonn [...] are estab1ished. These criteria extend those in [13-15] and [18].
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