Continuous dependence of the singular nonlinear Van der Pol equation solutions with respect to the boundary conditions: elements of \(p\)-regularity theory (Q2025690)
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scientific article; zbMATH DE number 7348207
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | Continuous dependence of the singular nonlinear Van der Pol equation solutions with respect to the boundary conditions: elements of \(p\)-regularity theory |
scientific article; zbMATH DE number 7348207 |
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Continuous dependence of the singular nonlinear Van der Pol equation solutions with respect to the boundary conditions: elements of \(p\)-regularity theory (English)
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14 May 2021
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The authors consider the two-point boundary value problem for the van der Pol equation: \[ x'' + \sigma(x^2 - 1)x' + x + x^p = 0,\quad x(0) = \nu, \quad x(2\pi) = \rho, \] where \(\sigma, \nu, \rho \in {\mathbb R}\). Using \(p\)-regularity theory sufficient conditions for the existence and continuous dependence of solutions of the BVP on the parameters \(\nu\) and \(\rho\) are obtained.
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\(p\)-regularity
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\(p\)-factor operator
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nonlinear boundary value problems
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implicit function theorem
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van der Pol equation
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