Existence And Uniqueness Of Nodal Solutions For Lidstone Eigenvalue Problems

The paper is concerned with nonlinear Lidstone eigenvalue problems of 2mth order ordinary differential equation(ODE)where m≥1 is integer, r∈R is parameter. By using eigenvalue theory and bifurcation techniques, we establish the theorem related to the existence of nodal solutions to (El). Furthermore, the uniqueness result of nodal solutions is given when dealing with the corresponding autonomous case, i.e.The main results of this paper are as follow:(i)The existence of nodal solutions for (El) is established.(ii)The uniqueness of nodal solutions for (E2) is discussed.