Classification of positive solutions of nonlinear differential equations (Q2770840)
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scientific article; zbMATH DE number 1704154
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | Classification of positive solutions of nonlinear differential equations |
scientific article; zbMATH DE number 1704154 |
Statements
13 February 2002
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oscillation
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nonoscillation
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quasilinear differential equations
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asymptotic behaviour
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Classification of positive solutions of nonlinear differential equations (English)
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Here, nonoscillatory solutions to a class of quasilinear differential equations of the form NEWLINE\[NEWLINE(r(t) \varphi(y'))'+ f(t,y)= 0,\quad t\geq 0,\tag{\(*\)}NEWLINE\]NEWLINE are classified according to their asymptotic behaviour as \(t\to\infty\). Necessary and sufficient conditions are given for such classification of solutions to \((*)\). Necessary and sufficient and sufficient conditions are given for the oscillation of all solutions to \((*)\).
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