Asymptotic bifurcation and second order elliptic equations on N
Annales de l'I.H.P. Analyse non linéaire, Volume 32 (2015) no. 6, p. 1259-1281
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This paper deals with asymptotic bifurcation, first in the abstract setting of an equation G(u)=λu, where G acts between real Hilbert spaces and λ, and then for square-integrable solutions of a second order non-linear elliptic equation on 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.

DOI : https://doi.org/10.1016/j.anihpc.2014.09.003
Classification:  35J91,  47J15
Keywords: Asymptotic linearity, Asymptotic bifurcation, Nonlinear elliptic equation
@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},
     publisher = {Elsevier},
     volume = {32},
     number = {6},
     year = {2015},
     pages = {1259-1281},
     doi = {10.1016/j.anihpc.2014.09.003},
     zbl = {1330.35187},
     mrnumber = {3425262},
     language = {en},
     url = {http://www.numdam.org/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, Volume 32 (2015) no. 6, pp. 1259-1281. doi : 10.1016/j.anihpc.2014.09.003. http://www.numdam.org/item/AIHPC_2015__32_6_1259_0/

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