Oscillation criteria of Kneser-Hille type for second-order differential equations with nonlinear perturbed terms (Q1767362)
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scientific article; zbMATH DE number 2143241
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | Oscillation criteria of Kneser-Hille type for second-order differential equations with nonlinear perturbed terms |
scientific article; zbMATH DE number 2143241 |
Statements
Oscillation criteria of Kneser-Hille type for second-order differential equations with nonlinear perturbed terms (English)
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10 March 2005
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The author studies a family of nonlinear second-order ordinary differential equations as a perturbation of a family of nonoscillatory linear Euler-type equations. He proves sufficient conditions of Kneser-Hille type which ensure that the perturbed equations become oscillatory (or remain nonoscillatory). The main tool is phase plane analysis of the corresponding system of first-order differential equations in polar coordinates.
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perturbed equation
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oscillation criteria
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nonoscilaltion criteria
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Euler equation
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