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A shooting argument with oscillation for semilinear elliptic radially symmetric equations

Published online by Cambridge University Press:  14 November 2011

C. K. R. T. Jones ,
T. Küpper  and
H. Plakties
C. K. R. T. Jones
Affiliation:
Department of Mathematics, University of Maryland, College Park, Maryland 20742, U.S.A.
T. Küpper
Affiliation:
Universität Hannover, Institut für Angewandte Mathematik, Welfengarten 1, D 3000 Hannover, Germany
H. Plakties
Affiliation:
Universität Dortmund, FB Mathematik, D 4600 Dortmund 50, Germany
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Synopsis

A new method is developed for finding radially symmetric solutions of semilinear elliptic problems by phase space methods. The basic idea is to formulate a shooting argument from initial conditions at r = 0 which involves encoding the oscillation information about the trajectories under consideration. The main theorem is applied to a particular nonlinearity and produces a cascade of solutions wherein the multiplicity increases with the number of zeros.

Type
Research Article
Information
Proceedings of the Royal Society of Edinburgh Section A: Mathematics , Volume 108 , Issue 1-2 , 1988 , pp. 165 - 180
Copyright
Copyright © Royal Society of Edinburgh 1988

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