On the qualitative behaviour of solutions of the equation \(\ddot x +f_ 1(x) \dot x+f_ 2(x)\dot x^ 2 +g(x)=0\) (Q1910841)
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scientific article; zbMATH DE number 859225
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | On the qualitative behaviour of solutions of the equation \(\ddot x +f_ 1(x) \dot x+f_ 2(x)\dot x^ 2 +g(x)=0\) |
scientific article; zbMATH DE number 859225 |
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On the qualitative behaviour of solutions of the equation \(\ddot x +f_ 1(x) \dot x+f_ 2(x)\dot x^ 2 +g(x)=0\) (English)
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13 May 1996
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The author develops a transformation which transforms the ordinary differential equation \(\ddot x + f_1(x) \dot x + f_2(x) \dot x^2 + g(x) = 0\) into a Liénard equation whose properties are well-known. The periodicity and stability of solutions are then discussed. The work was prompted by a paper by \textit{H. L. Guidorizzi} [J. Math. Anal. Appl. 176, 11-23 (1993; Zbl 0778.34019)].
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transformation
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Liénard equation
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periodicity
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stability
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