Bifurcation from the essential spectrum without sign condition on the nonlinearity

Authors
Citation
M. Kunze, Bifurcation from the essential spectrum without sign condition on the nonlinearity, P RS EDIN A, 131, 2001, pp. 927-943
Citations number
19
Language
INGLESE
art.tipo
Article
Categorie Soggetti
Mathematics
Journal title
PROCEEDINGS OF THE ROYAL SOCIETY OF EDINBURGH SECTION A-MATHEMATICS
ISSN journal
0308-2105 → ACNP
Volume
131
Year of publication
2001
Part
4
Pages
927 - 943
Database
ISI
SICI code
0308-2105(2001)131:<927:BFTESW>2.0.ZU;2-R
Abstract
We study a problem from nonlinear optics that leads to an integro-different ial equation which can be written as the abstract bifurcation problem Au = lambda Lu + del phi (u). For such a type of equation, a general theorem on the bifurcation of solutions from the essential spectrum is proved. The hyp othesis that phi is non-negative (as is usually assumed) could be omitted a nd replaced by other conditions that allow us to use the results for the pa rticular example. We also indicate applications to semilinear elliptic equa tions.