Some Extended Nabla and Delta Hardy–Copson Type Inequalities with Applications in Oscillation Theory

AbstractIn this work, we present new necessary and sufficient conditions for the oscillation of a class of second-order neutral delay impulsive differential equations. Our oscillation results complement, simplify and improve recent results on oscillation theory of this type of nonlinear neutral impulsive differential equations that appear in the literature. An example is provided to illustrate the value of the main results.

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Ladde, G. S.; Lakshmikantham, V.; Zhang, B. G., Oscillation Theory of Differential Equations with Deviating Arguments. New York, Basel, Marcl Dekker 1987. VI, 308 pp., $ 107.50. ISBN 0-8247-7738-7 (Pure and Applied Mathematics: A Series of Monographs and Textbooks 110)

ZAMM ‐ Journal of Applied Mathematics and Mechanics / Zeitschrift für Angewandte Mathematik und Mechanik ◽

10.1002/zamm.19880681230 ◽

1988 ◽

Vol 68 (12) ◽

pp. 655-655

Author(s):

G. Schmidt

Keyword(s):

New York ◽

Differential Equations ◽

Applied Mathematics ◽

Oscillation Theory ◽

Deviating Arguments

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A note on the complex oscillation theory of non- homogeneous linear differential equations

Results in Mathematics ◽

10.1007/bf03323172 ◽

1990 ◽

Vol 18 (3-4) ◽

pp. 282-285 ◽

Cited By ~ 5

Author(s):

Ilpo Laine

Keyword(s):

Differential Equations ◽

Oscillation Theory ◽

Linear Differential Equations ◽

Complex Oscillation ◽

Linear Differential ◽

Homogeneous Linear

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Dynamic behaviors of a nonautonomous predator–prey system with Holling type II schemes and a prey refuge

Advances in Difference Equations ◽

10.1186/s13662-021-03222-1 ◽

2021 ◽

Vol 2021 (1) ◽

Author(s):

Yumin Wu ◽

Fengde Chen ◽

Caifeng Du

Keyword(s):

Lyapunov Function ◽

Differential Equations ◽

Comparison Theorem ◽

Sufficient Conditions ◽

Oscillation Theory ◽

Type Ii ◽

Prey Refuge ◽

Predator Prey ◽

Predator Prey Model ◽

Prey System

AbstractIn this paper, we consider a nonautonomous predator–prey model with Holling type II schemes and a prey refuge. By applying the comparison theorem of differential equations and constructing a suitable Lyapunov function, sufficient conditions that guarantee the permanence and global stability of the system are obtained. By applying the oscillation theory and the comparison theorem of differential equations, a set of sufficient conditions that guarantee the extinction of the predator of the system is obtained.

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