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We consider the nonlinear eigenvalue problem , , , , where , , and is a bifurcation parameter. Here, and () are constants. This equation is related to the mathematical model of animal dispersal and invasion, and is parameterized by the maximum norm of the solution associated with and is written as . Since contains both power nonlinear term and oscillatory term , it seems interesting to investigate how the shape of is affected by . The purpose of this paper is to characterize the total shape of by and . Precisely, we establish three types of shape of , which seem to be new.

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