This paper deals with asymptotic bifurcation, first in the abstract setting of an equation , where G acts between real Hilbert spaces and , and then for square-integrable solutions of a second order non-linear elliptic equation on . 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.
@article{AIHPC_2015__32_6_1259_0, author = {Stuart, C.A.}, title = {Asymptotic bifurcation and second order elliptic equations on $ {\mathbb{R}}^{N}$ }, journal = {Annales de l'I.H.P. Analyse non lin\'eaire}, volume = {32}, year = {2015}, pages = {1259-1281}, doi = {10.1016/j.anihpc.2014.09.003}, mrnumber = {3425262}, zbl = {1330.35187}, language = {en}, url = {http://dml.mathdoc.fr/item/AIHPC_2015__32_6_1259_0} }
Stuart, C.A. Asymptotic bifurcation and second order elliptic equations on $ {\mathbb{R}}^{N}$ . Annales de l'I.H.P. Analyse non linéaire, Tome 32 (2015) pp. 1259-1281. doi : 10.1016/j.anihpc.2014.09.003. http://gdmltest.u-ga.fr/item/AIHPC_2015__32_6_1259_0/
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