Asymptotic bifurcation and second order elliptic equations on

  • C.A. Stuart

    Station 8, Section de mathématiques, Ecole Polytechnique Fédérale Lausanne, CH-1015 Lausanne, Switzerland


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.

Cite this article

C.A. Stuart, Asymptotic bifurcation and second order elliptic equations on . Ann. Inst. H. Poincaré Anal. Non Linéaire 32 (2015), no. 6, pp. 1259–1281

DOI 10.1016/J.ANIHPC.2014.09.003