Bifurcation from zero or infinity in nonlinearizable Sturm–Liouville problems with indefinite weight

Abstract

In this paper, we consider bifurcation from zero or infinity of nontrivial solutions of the nonlinear Sturm–Liouville problem with indefinite weight. This problem is mainly important because of it is related with a selection-migration model in genetic population. We show the existence of four families of unbounded continua of nontrivial solutions to this problem bifurcating from intervals of the line of trivial solutions or the line $\mathbb{R} \times \{\infty\}$ (these intervals are called bifurcation intervals). Moreover, these global continua have the usual nodal properties in some neighborhoods of bifurcation intervals.

Keywords

• nonlinear sturm–liouville problem
• indefinite weight
• population genetics
• selection-migration model
• bifurcation point
• bifurcation interval
• global continua