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The existence of infinitely many bifurcating branches

Published online by Cambridge University Press:  14 November 2011

Hans-Jörg Ruppen
Hans-Jörg Ruppen
Affiliation:
Niedergampelstrasse, 3945 Gampel, Switzerland
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Synopsis

We consider the non-linear problem −Δu(x)−f(x, u(x)) = λu(x) for x ∈ℝN and u ∈ W1,2(ℝN). We show that, under suitable conditions on f, there exist infinitely many branches all bifurcating from the lowest point of the continuous spectrum λ = 0. The method used in the proof is based on a theorem of Ljusternik-Schnirelman type for the free case.

Type
Research Article
Information
Proceedings of the Royal Society of Edinburgh Section A: Mathematics , Volume 101 , Issue 3-4 , 1985 , pp. 307 - 320
Copyright
Copyright © Royal Society of Edinburgh 1985

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