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Displaying 1621 – 1640 of 1670

Oscillatory and asymptotic behaviour of solutions of advanced functional equations

Jozef Džurina (1993)

Archivum Mathematicum

In this paper we compare the asymptotic behaviour of the advanced functional equation $L_{n} u (t) - F (t, u [g (t)]) = 0$ with the asymptotic behaviour of the set of ordinary functional equations $α_{i} u (t) - F (t, u (t)) = 0 .$ On the basis of this comparison principle the sufficient conditions for property (B) of equation (*) are deduced.

Oscillatory and asymptotic properties of the solutions of a class of operator-differential equations.

D. D. Bainov, M. D. Dimitrova, A. D. Myshkis (1994)

Revista Matemática de la Universidad Complutense de Madrid

Oscillatory and asymptotic properties of third and fourth order linear differential equations

Ján Ohriska (1989)

Czechoslovak Mathematical Journal

Oscillatory and non oscillatory criteria for the systems of two linear first order two by two dimensional matrix ordinary differential equations

Gevorg Avagovich Grigorian (2018)

Archivum Mathematicum

The Riccati equation method is used for study the oscillatory and non oscillatory behavior of solutions of systems of two first order linear two by two dimensional matrix differential equations. An integral and an interval oscillatory criteria are obtained. Two non oscillatory criteria are obtained as well. On an example, one of the obtained oscillatory criteria is compared with some well known results.

Oscillatory and non-oscillatory criteria for linear four-dimensional Hamiltonian systems

Gevorg A. Grigorian (2021)

Mathematica Bohemica

The Riccati equation method is used to study the oscillatory and non-oscillatory behavior of solutions of linear four-dimensional Hamiltonian systems. One oscillatory and three non-oscillatory criteria are proved. Examples of the obtained results are compared with some well known ones.

Oscillatory and nonoscillatory properties of solutions of the differential equation $y^{(4)} + P (t) y " + Q (t) y = 0$

Ján Regenda (1978)

Mathematica Slovaca

Oscillatory and nonoscillatory solutions for first order impulsive differential inclusions

Mouffak Benchohra, Abdelghani Ouahab (2005)

Commentationes Mathematicae Universitatis Carolinae

In this paper we discuss the existence of oscillatory and nonoscillatory solutions of first order impulsive differential inclusions. We shall rely on a fixed point theorem of Bohnenblust-Karlin combined with lower and upper solutions method.

Oscillatory and nonoscillatory solutions for first order impulsive dynamic inclusions on time scales

Mouffak Benchohra, Samira Hamani, Johnny Henderson (2007)

Archivum Mathematicum

In this paper we discuss the existence of oscillatory and nonoscillatory solutions for first order impulsive dynamic inclusions on time scales. We shall rely of the nonlinear alternative of Leray-Schauder type combined with lower and upper solutions method.

Oscillatory and nonoscillatory solutions of neutral differential equations

Satoshi Tanaka (2000)

Annales Polonici Mathematici

Neutral differential equations are studied. Sufficient conditions are obtained to have oscillatory solutions or nonoscillatory solutions. For the existence of solutions, the Schauder-Tikhonov fixed point theorem is used.

Oscillatory behavior of higher order neutral differential equation with multiple functional delays under derivative operator

R.N. Rath, K.C. Panda, S.K. Rath (2022)

Archivum Mathematicum

In this article, we obtain sufficient conditions so that every solution of neutral delay differential equation ${(y (t) - \sum_{i = 1}^{k} p_{i} (t) y (r_{i} (t)))}^{(n)} + v (t) G (y (g (t))) - u (t) H (y (h (t))) = f (t)$ oscillates or tends to zero as $t \to \infty$ , where, $n \geq 1$ is any positive integer, $p_{i}$ , $r_{i} \in C^{(n)} ([0, \infty), ℝ)$ and $p_{i}$ are bounded for each $i = 1, 2, \dots, k$ . Further, $f \in C ([0, \infty), ℝ)$ , $g$ , $h$ , $v$ , $u \in C ([0, \infty), [0, \infty))$ , $G$ and $H \in C (ℝ, ℝ)$ . The functional delays $r_{i} (t) \leq t$ , $g (t) \leq t$ and $h (t) \leq t$ and all of them approach $\infty$ as $t \to \infty$ . The results hold when $u \equiv 0$ and $f (t) \equiv 0$ . This article extends, generalizes and improves some recent results, and further answers some unanswered questions from the literature.

Oscillatory behavior of iterative linear ordinary differential equations depends on their order

František Neuman (1986)

Archivum Mathematicum

Oscillatory behavior of quasilinear neutral delay dynamic equations on time scales.

Han, Zhenlai, Sun, Shurong, Li, Tongxing, Zhang, Chenghui (2010)

Advances in Difference Equations [electronic only]

Oscillatory behavior of second-order neutral difference equations with positive and negative coefficients.

Thandapani, Ethiraju, Thangavelu, Krishnan, Chandrasekaran, Ekambaram (2009)

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

Oscillatory behaviour of a class of nonlinear second order mixed difference equations.

Tripathy, A.K. (2010)

Electronic Journal of Qualitative Theory of Differential Equations [electronic only]

Oscillatory behaviour of a higher order nonlinear neutral delay type functional differential equation with oscillating coefficients

Yaşar Bolat, Ömer Akin (2005)

Czechoslovak Mathematical Journal

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.

Oscillatory behaviour of certain difference equations

Said R. Grace (2000)

Mathematica Slovaca

Oscillatory behaviour of nonlinear differential equations with deviating arguments

Bikkar S. Lalli (1987)

Archivum Mathematicum

Oscillatory behaviour of solutions of forced neutral differential equations

N. Parhi, P. K. Mohanty (1996)

Annales Polonici Mathematici

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.

Oscillatory behaviour of solutions of nonlinear higher order neutral differential equations

N. Parhi, Radhanath N. Rath (2004)

Mathematica Bohemica

Oscillatory behaviour of solutions of two-dimensional differential systems with deviated arguments.

Koplatadze, R., Partsvania, N. (1999)

Georgian Mathematical Journal

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