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SOME SINGULARLY PERTURBED PROBLEMS ON ANNULI AND A COUNTEREXAMPLE TO A PROBLEM OF GIDAS, NI AND NIRENBERG

Published online by Cambridge University Press:  01 May 1997

E. N. DANCER
E. N. DANCER
Affiliation:
School of Mathematics and Statistics, University of Sydney, N.S.W. 2006, Australia
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Abstract

In this note we discuss the radial positive solutions of

formula here

where D is the annulus {s∈Rn [ratio ]b<|s|<1}. Here 0<b<1, n[ges ]2, and g[ratio ]R→R is a suitable C1 function with g(0)[ges ]0 but with g changing sign. We answer a question on page 223 of the original Gidas–Ni–Nirenberg paper [8], by showing that the maximum of these solutions occurs at a point sε, where |sε|→b as ε→0. This also shows that the non-negativity condition in the result on page 223 of [8] is necessary.

Type
Research Article
Information
Bulletin of the London Mathematical Society , Volume 29 , Issue 3 , May 1997 , pp. 322 - 326
Copyright
© The London Mathematical Society 1997

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