This is a part of the Handbook of Differential Equations (A.
Canada, P. Drabek, A. Fonda, editors), where recent results in
the qualitative theory of half-linear differential equations
are presented.

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Half-linear differential equations

Preface. 1. Preliminaries. 2. Oscillation and Nonoscillation of Linear Ordinary Differential Equations. 3. Oscillation and Nonoscillation of Half-Linear Differential Equations. 4. Oscillation Theory for Superlinear Differential Equations. 5. Oscillation Theory for Sublinear Differential Equations. 6. Further Results on the Oscillation of Differential Equations. 7. Oscillation Results for Differential Systems. 8. Asymptotic Behavior of Solutions of Certain Differential Equations. 9. Miscellaneous Topics. 10. Nonoscillation Theory for Multivalued Differential Equations. Subject Index.

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Oscillation Theory for Second Order Linear, Half-Linear, Superlinear and Sublinear Dynamic Equations

This book summarizes the qualitative theory of differential equations with or without delays, collecting recent oscillation studies important to applications and further developments in mathematics, physics, engineering, and biology. The authors address oscillatory and nonoscillatory properties of first-order delay and neutral delay differential equations, second-order delay and ordinary differential equations, higher-order delay differential equations, and systems of nonlinear differential equations. The final chapter explores key aspects of the oscillation of dynamic equations on time scales-a new and innovative theory that accomodates differential and difference equations simultaneously.

Nonoscillation and Oscillation Theory for Functional Differential Equations

Oscillation of third-order neutral differential equations

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Comparison theorems for functional differential equations with deviating arguments

The equation to be considered iswhere pi(t), 0≦i≦n, and q(t) are continuous and positive on some half-line [a, ∞). It is known that (*) always has “strictly monotone” nonoscillatory solutions defined on [a, ∞), so that of particular interest is the extreme situation in which such strictly monotone solutions are the only possible nonoscillatory solutions of (*). In this paper sufficient conditions are given for this situation to hold for (*). The structure of the solution space of (*) is also studied.

https://www.cambridge.org/core/services/aop-cambridge-core/content/view/S0308210500015328

Oscillatory and asymptotic behaviour of solutions of a class of linear ordinary differential equations

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Manabu Naito

Papers

Comparison theorems for functional differential equations with deviating arguments

Oscillatory and asymptotic behaviour of solutions of a class of linear ordinary differential equations

Oscillation criteria for general linear ordinary differential equations.

Integral averages and the asymptotic behavior of solutions of second order ordinary differential equations

On Fourth‐Order Non‐Linear Oscillations