Branches of forced oscillations in degenerate systems of second-order ODEs
β Scribed by Marta Lewicka; Marco Spadini
- Publisher
- Elsevier Science
- Year
- 2008
- Tongue
- English
- Weight
- 215 KB
- Volume
- 68
- Category
- Article
- ISSN
- 0362-546X
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π SIMILAR VOLUMES
This paper discusses the application of the "patching" method to a nonlinear differential equation. The case chosen is a simple one and very representative of the difficulties involved.
We discuss the existence of positive solutions of the system where the nonlinearities f and g satisfy a superlinearity condition at both 0 and β. Our main result is the proof of a priori bounds for the eventual solutions. As an application, we consider the Dirichlet problem in an annulus for system
## Abstract In this paper, we establish some new criteria for the oscillation of second order forced nonlinear differential equations (__r__ (__t__ )__x__ β²(__t__ ))β² + __p__ (__t__ )__x__ β²(__t__ ) + __q__ (__t__ )__f__ (__x__ (__t__ )) = __e__ (__t__ ) in both cases when __q__ (__t__ ) < 0 and __