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Transversality and separation of zeros in second order differential equations

Laister, Robert; Beardmore, R. E.

Transversality and separation of zeros in second order differential equations Thumbnail


Authors

R. E. Beardmore



Abstract

Sufficient conditions on the non-linearity f are given which ensure that non-trivial solutions of second order differential equations of the form Lu = f(t, u) have a finite number of transverse zeros in a given finite time interval. We also obtain a priori lower bounds on the separation of zeros of solutions. In particular our results apply to non-Lipschitz non-linearities. Applications to non-linear porous medium equations are considered, yielding information on the existence and strict positivity of equilibrium solutions in some important classes of equations.

Citation

Laister, R., & Beardmore, R. E. (2003). Transversality and separation of zeros in second order differential equations. Proceedings of the American Mathematical Society, 131(1), 209-218. https://doi.org/10.1090/S0002-9939-02-06546-2

Journal Article Type Article
Publication Date Jan 1, 2003
Deposit Date Jul 7, 2010
Publicly Available Date May 24, 2016
Journal Proceedings of the American Mathematical Society
Print ISSN 0002-9939
Publisher American Mathematical Society
Peer Reviewed Peer Reviewed
Volume 131
Issue 1
Pages 209-218
DOI https://doi.org/10.1090/S0002-9939-02-06546-2
Keywords differential equations, transverse zeros, non-Lipschitz non-linearity, separation of zeros, porous medium equations
Public URL https://uwe-repository.worktribe.com/output/1073723
Publisher URL http://dx.doi.org/10.1090/S0002-9939-02-06546-2

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