Bifurcation Of A Class Of Ordinary Differential Equations

In this paper,the bifurcation phenomenon of a class of second-order ordinary differential equations under Neumann boundary conditions is mainly studied.By constructing a completely continuous linear operator and connecting with the eigenvalues of linearized equations,the existence of bifurcation points is proved.Then,the structure of bifurcation branch is studied,and the global bifurcation theorem and unilateral global bifurcation theorem of the equation are established.Finally,the existence of nodal solutions of the equation in nine cases is solved.