BIFURCATIONS WITH MULTI-DIMENSIONAL KERNEL IN A CHEMOTAXIS-GROWTH SYSTEM

抄録

We study the bifurcation problem for a chemotaxis-growth system with logistic growth in a two-dimensional rectangular domain. We apply the local bifurcation theorem by Ambrosetti and Prodi that does not require one-dimensional degeneration of the linearized operator around trivial solutions. We then obtain bifurcation solutions with two- and three-dimensional degeneration indicating spatially regular nesting patterns.