Transversality and separation of zeros in second order differential equations

Laister, Robert; Beardmore, R. E.

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.

• 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
• Electronic ISSN: 1088-6826
• 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
• Contract Date: May 24, 2016