Proceedings of the American Mathematical Society

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ISSN 1088-6826(e) ISSN 0002-9939(p)

Transversality and separation of zeros in second order differential equations

Author(s): R. Laister; R. E. Beardmore
Journal: Proc. Amer. Math. Soc. 131 (2003), 209-218.
MSC (2000): Primary 34C10, 34A12, 34A34; Secondary 34B15, 34B60
Posted: May 17, 2002
MathSciNet review: 1929040
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Abstract: Sufficient conditions on the non-linearity are given which ensure that non-trivial solutions of second order differential equations of the form 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.

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