Bifurcation points of a degenerate elliptic boundary-value problem

  • Gilles Evéquoz

    Ecole Polytechnique Federale, Lausanne, Switzerland
  • Charles A. Stuart

    Ecole Polytechnique Federale, Lausanne, Switzerland

Abstract

We consider the nonlinear elliptic eigenvalue problem

where is a bounded open subset of and with and . The ellipticity is degenerate in the sense that and for but . We show that there is vertical bifurcation at all points in the interval Bifurcation also occurs at any eigenvalues of the linearized problem that are below . Our treatment is based on recent results concerning the bifurcation points of equations with nonlinearities that are Hadamard differentiable, but not Fréchet differentiable.

Cite this article

Gilles Evéquoz, Charles A. Stuart, Bifurcation points of a degenerate elliptic boundary-value problem. Atti Accad. Naz. Lincei Cl. Sci. Fis. Mat. Natur. 17 (2006), no. 4, pp. 309–334

DOI 10.4171/RLM/471