Non-linear Sturm-Liouville problems with no secondary bifurcation

Abstract

SynopsisThe paper is concerned with giving sufficient conditions that in the non-linear boundary-value problemthere should be no secondary bifurcation, i.e. that, given a branch of solutions (u, λ) bifurcating from the trivial solution, there should be no further bifurcation on that branch. Sufficient conditions on G are given which include, for example, Kolodner's problem of the motion of a heavy rotating string.