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The paper is concerned with oscillation properties of $n$ -th order neutral differential equations of the form ${[x (t) + c x (τ (t))]}^{(n)} + q (t) f (x (σ (t))) = 0, t \geq t_{0} > 0,$ where $c$ is a real number with $| c | \neq 1$ , $q \in C ([t_{0}, \infty), ℝ)$ , $f \in C (ℝ, ℝ)$ , $τ, σ \in C ([t_{0}, \infty), ℝ_{+})$ with $τ (t) < t$ and ${lim}_{t \to \infty} τ (t) = {lim}_{t \to \infty} σ (t) = \infty$ . Sufficient conditions are established for the existence of positive solutions and for oscillation of bounded solutions of the above equation. Combination of these conditions provides necessary and sufficient conditions for oscillation of bounded solutions of the equation. Furthermore, the results are generalized to equations in which...

Bounded solutions: differential vs difference equations.

Mawhin, Jean (2009)

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

Bounded solutions for second-order ordinary differential equations.

Naulin, Raúl (1999)

Divulgaciones Matemáticas

Bounded solutions for singular boundary value problems

Marius Dădărlat (1987)

Mathematica Slovaca

Bounded solutions of abstract equations.

Dorogovtsev, A. Ya. (2000)

Novi Sad Journal of Mathematics

Bounded solutions of Carathéodory differential inclusions: a bound sets approach.

Andres, Jan, Malaguti, Luisa, Taddei, Valentina (2003)

Abstract and Applied Analysis

Bounded solutions of second order functional differential equations

Staněk, Svatoslav (1991)

Acta Universitatis Palackianae Olomucensis. Facultas Rerum Naturalium. Mathematica

Bounded solutions of second order semicoercive evolution equations in a Hilbert space and of nonlinear telegraph equations.

Mawhin, J. (2000)

Rendiconti del Seminario Matematico

Bounded solutions of systems of differential equations with impulses

S. G. Hristova, D. D. Bainov (1988)

Annales Polonici Mathematici

Bounded solutions on the Real line to non-autonomous Riccati Equations

Giuseppe Da Prato, Akira Ichikawa (1985)

Atti della Accademia Nazionale dei Lincei. Classe di Scienze Fisiche, Matematiche e Naturali. Rendiconti Lincei. Matematica e Applicazioni

Si dà un risultato di esistenza e unicità di una soluzione limitata in $]-\infty,+\infty[$ per un'equazione di Riccati infinito-dimensionale.

Bounded solutions to a system of second order ODEs and the Whitney pendulum

Oleg Zubelevich (2015)

Applicationes Mathematicae

We give an existence theorem for bounded solutions to a system of second order ODEs. Dynamical applications are considered.

Bounded solutions to perturbed nonlinear systems and asymptotic relationships.

Athanassios G. Kartsatos (1975)

Journal für die reine und angewandte Mathematik

Boundedness and almost periodicity for some state-dependent delay differential equations.

Dads, El Hadi Ait, Ezzinbi, Khalil (2002)

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

Boundedness and asymptotic stability in the large of solutions of an ordinary differential system $y^{'} = f (t, y, y^{'})$ .

Venkatesulu, M., Srinivasu, P.D.N. (1992)

Journal of Applied Mathematics and Stochastic Analysis

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Bounded index, entire solutions of ordinary differential equations and summability methods.

Bounded nonoscillatory solutions of neutral type difference systems.

Bounded oscillation of higher order neutral differential equations with oscillating coefficients.

Bounded oscillation of nonlinear neutral differential equations of arbitrary order