caa a22 4500 475797280 CHVBK 20180406123728.0 cr unu---uuuuu 170329e20000901xx s 000 0 eng 10.1007/PL00001522 doi (NATIONALLICENCE)springer-10.1007/PL00001522 Crooks E. C. M. Balliol College, Oxford 0X1 3BI, U.K., e-mail: elaine.crooks@balliol.ox.ac.uk, UK aut Bifurcation from the essential spectrum for almost-periodic perturbations of Hill's equation [Elektronische Daten] [E. C. M. Crooks] Abstract.: We show that the infimum of the essential spectrum of the linearisation of the equation¶¶ $ -\ddot{u}(x) + V(x)u(x) -r(x) |u(x) |^{p-1} u(x) = \lambda u(x) $ (1)¶¶ is a bifurcation point for (1). Here the potential V is periodic and the function r almost-periodic. Thus (1) is an almost-periodic perturbation of Hill's equation. Bifurcation results of Küpper and Stuart are combined with existence theory for almost-periodic problems developed by Serra, Tarallo and Terracini. Birkhäuser Verlag, Basel,, 2000 Key words. Hill's equation, almost-periodicity, bifurcation, essential spectrum, Mountain Pass Lemma nationallicence https://doi.org/10.1007/PL00001522 text/html Onlinezugriff via DOI 1 research-article jats NATIONALLICENCE 856 40 https://doi.org/10.1007/PL00001522 text/html Onlinezugriff via DOI NATIONALLICENCE 100 1- Crooks E. C. M. Balliol College, Oxford 0X1 3BI, U.K., e-mail: elaine.crooks@balliol.ox.ac.uk, UK aut Metadata rights reserved Springer special CC-BY-NC licence nationallicence BK010053 XK010053 XK010000 NATIONALLICENCE NATIONALLICENCE NL-springer