Multiple limit point bifurcation

Abstract

In this paper we present a new bifurcation or branching phenomenon which we call multiple limit point bifurcation. It is of course well known that bifurcation points of some nonlinear functional equation G(u, λ) = 0 are solutions (u_0, λ_0) at which two distinct smooth branches of solutions, say [u(ε), λ(ε)] and [u^(ε), λ^(ε)], intersect nontangentially. The precise nature of limit points is less easy to specify but they are also singular points on a solution branch; that is, points (u_0, λ_0) = (u(0), λ(0)), say, at which the Frechet derivative G_u^0 ≡ G_u(u_0, λ_0) is singular.

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