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Multiplicity of solutions to a degenerate diffusion problem

✍ Scribed by J Garcı́a-Melián; J.Sabina de Lis

Publisher
Elsevier Science
Year
2003
Tongue
English
Weight
264 KB
Volume
53
Category
Article
ISSN
0362-546X

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✦ Synopsis

In this paper it is shown that the Dirichlet problempu = f(u); u @B = 0 in a ball B ⊂ R N , loses the property of uniqueness of positive solutions u under the sole condition maxB u → u0 as → + ∞, with u0 ¿ 0 certain preÿxed zero of f, provided p ¿ k + 1; k being the order of u0, what is in contrast with the so-called "nondegenerate case" p 6 k + 1 where such hypothesis implies uniqueness. This also proves that a slightly stronger convergence condition for uniqueness introduced by the authors in a previous work cannot be relaxed.

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