Generating an arbitrarily large number of isolas in a superlinear indefinite problem

Abstract

This paper analyzes the effect of an asymmetric weight on the bifurcation diagrams relative to a class of superlinear indefinite problems which admit an arbitrarily high number of positive solutions for certain values of the parameters involved in their formulation. The main result is that the secondary bifurcations which occur in the symmetric case (see López-Gómez et al. (2014)) give rise, in the asymmetric case, to bounded components of solutions, whose number grows arbitrarily as the number of the solutions of the problem grows.