On necessary conditions for the existence of local solutions to singular nonlinear ordinary differential equations and inequalities (Q1810264)
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scientific article; zbMATH DE number 1928351
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | On necessary conditions for the existence of local solutions to singular nonlinear ordinary differential equations and inequalities |
scientific article; zbMATH DE number 1928351 |
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On necessary conditions for the existence of local solutions to singular nonlinear ordinary differential equations and inequalities (English)
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15 June 2003
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The author obtains conditions for the nonexistence of global solutions, and he estimates the existence time for local solutions to the problem \[ {d^k y\over dt^k}\geq a_1(t)| y|^{q_1}+ a_2(t)| y|^{q_2}+\cdots+ a_n(t)| y|^{q_n}. \] For the proof, the author uses the method of trial functions developed by Mitidieri and Pokhozhaev.
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method of trial functions
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nonexistence theorem
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necessary condition
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