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Bifurcation from the essential spectrum without sign condition on the nonlinearity

Published online by Cambridge University Press:  12 July 2007

M. Kunze
M. Kunze
Affiliation:
Mathematisches Institut der Universität Köln, Weyertal 86, D-50931 Köln, Germany
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Abstract

We study a problem from nonlinear optics that leads to an integro-differential equation which can be written as the abstract bifurcation problem Au = λLu + ∇φ(u). For such a type of equation, a general theorem on the bifurcation of solutions from the essential spectrum is proved. The hypothesis that φ is non-negative (as is usually assumed) could be omitted and replaced by other conditions that allow us to use the results for the particular example. We also indicate applications to semilinear elliptic equations.

Type
Research Article
Information
Proceedings of the Royal Society of Edinburgh Section A: Mathematics , Volume 131 , Issue 4 , August 2001 , pp. 927 - 943
Copyright
Copyright © Royal Society of Edinburgh 2001

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