Global and Local Structures of Bifurcation Curves of ODE with Nonlinear Diffusion

[摘要] We consider the nonlinear eigenvalue problem , , , , where , , andis a bifurcation parameter. Here,and() are constants. This equation is related to the mathematical model of animal dispersal and invasion, andis parameterized by the maximum normof the solutionassociated withand is written as . Sincecontains both power nonlinear termand oscillatory term , it seems interesting to investigate how the shape ofis affected by . The purpose of this paper is to characterize the total shape ofbyand . Precisely, we establish three types of shape of , which seem to be new.

[学科分类] 几何与拓扑