Bifurcations of One-Dimensional reaction-Diffusion equations

Bifurcations of a class of one-dimensional reaction–diffusion equations of the form u″+μu-uk=0, where μ is a parameter, 2≤k∈Z+, with boundary value condition u(0)=u(π)=0, are investigated. Using the singularity theory based on the Liapunov–Schmidt reduction, some characterization results are obtained.