Oscillation of solutions of second-order nonlinear self-adjoint differential equations (Q1433349)
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scientific article; zbMATH DE number 2075631
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | Oscillation of solutions of second-order nonlinear self-adjoint differential equations |
scientific article; zbMATH DE number 2075631 |
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Oscillation of solutions of second-order nonlinear self-adjoint differential equations (English)
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15 June 2004
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The paper investigates the oscillation problem for the nonlinear selfadjoint differential equation \((a(t)x')'+b(t)g(x)=0\), where \(g(x)\) satisfies the signum condition \(xg(x)>0\), \(x\neq 0\). It is shown that certain growth conditions on \(g(x)\) play an essential role in deciding whether nontrivial solutions are oscillatory or not. Proofs use Sturm's comparison method and phase plane analysis of systems of Liénard type.
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oscillation
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nonlinear selfadjoint differential equations
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Sturm's comparison method
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phase plane
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Liénard systems
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