Abstract
is taken as the boundary condition at infinity. Our interest in this problem derives from the fact that it provides an example of bifurcation from the essential spectrum. The terms “bifurcation from the essential spectrum” or “singular bifurcation” have recently been used to describe the following situation: Suppose A is a self-adjoint Hilbert space operator arising from a singular elliptic boundary value problem so that the essential spectrum of A may be non-empty. When A is perturbed by a nonlinearity F such that F(u) vanishes of higher order for u + 0, the points of the essential spectrum of A are candidates for bifurcation points of the nonlinear eigenvalue problem
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