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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
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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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Additional Information:
R.
Laister
Affiliation:
School of Mathematical Sciences, University of the West of England, Frenchay Campus, Bristol, England BS16 1QY
Email:
Robert.Laister@uwe.ac.uk
R.
E.
Beardmore
Affiliation:
Department of Mathematics, Imperial College, London, England SW7 2BZ
Email:
R.Beardmore@ic.ac.uk
DOI:
10.1090/S0002-9939-02-06546-2
PII:
S 0002-9939(02)06546-2
Keywords:
Differential equations,
transverse zeros,
non-Lipschitz non-linearity,
separation of zeros,
porous medium equations
Received by editor(s):
May 29, 2001
Received by editor(s) in revised form:
August 25, 2001
Posted:
May 17, 2002
Communicated by:
Carmen C. Chicone
Copyright of article:
Copyright
2002,
American Mathematical Society
Forward Citation(s): Information for authors on submitting citations The following works have cited this article R.E. Beardmore and R. Laister, Sequential and Continuum Bifurcations in Degenerate Elliptic Equations, Proc. Amer. Math. Soc. 132 (2004), 165-174.
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