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Perturbations near zero of the leading coefficient of solutions to a nonlinear differential equation


Author: Vadim Komkov
Journal: Proc. Amer. Math. Soc. 99 (1987), 93-104
MSC: Primary 34C15; Secondary 03H05, 26E35, 58F05
DOI: https://doi.org/10.1090/S0002-9939-1987-0866436-3
MathSciNet review: 866436
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Abstract: The equation

$\displaystyle \frac{d}{{dt}}\left( {a\left( t \right) \cdot \psi \left( x \righ... ...eft( x \right) \cdot \frac{{dx}}{{dt}} + c\left( t \right)x = g\left( t \right)$

that generalizes the more commonly studied selfadjoint second order equation

$\displaystyle \frac{d}{{dt}}\left( {a\left( t \right)\frac{{dx}}{{dt}}} \right) + c\left( t \right)x = g\left( t \right)$

occurs in celestial dynamics, in the study of gyroscopic systems, and in other problems of nonlinear mechanics. Using techniques of nonstandard analysis we derive some properties of the "duck"-type cycles for the solutions of this equation.

References [Enhancements On Off] (What's this?)

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Additional Information

DOI: https://doi.org/10.1090/S0002-9939-1987-0866436-3
Article copyright: © Copyright 1987 American Mathematical Society