Asymptotic bifurcation and second order elliptic equations on R-N

This paper deals with asymptotic bifurcation, first in the abstract setting of an equation G(u) = lambda u, where G acts between real Hilbert spaces and lambda is an element of R, and then for square-integrable solutions of a second order non-linear elliptic equation on R-N. The novel feature of this work is that G is not required to be asymptotically linear in the usual sense since this condition is not appropriate for the application to the elliptic problem. Instead, G is only required to be Hadamard asymptotically linear and we give conditions ensuring that there is asymptotic bifurcation at eigenvalues of odd multiplicity of the H-asymptotic derivative which are sufficiently far from the essential spectrum. The latter restriction is justified since we also show that for some elliptic equations there is no asymptotic bifurcation at a simple eigenvalue of the H-asymptotic derivative if it is too close to the essential spectrum. (C) 2014 Elsevier Masson SAS. All rights reserved.


Publié dans:
Annales De L Institut Henri Poincare-Analyse Non Lineaire, 32, 6, 1259-1281
Année
2015
Publisher:
Amsterdam, Elsevier Science Bv
ISSN:
0294-1449
Mots-clefs:
Laboratoires:




 Notice créée le 2016-02-16, modifiée le 2018-09-13


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