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.

Published in:
Annales De L Institut Henri Poincare-Analyse Non Lineaire, 32, 6, 1259-1281
Amsterdam, Elsevier Science Bv

 Record created 2016-02-16, last modified 2018-12-03

Rate this document:

Rate this document:
(Not yet reviewed)