Nodal solutions to nonlinear eigenvalue problems on time scales

Using global bifurcation theory, we obtain the existence of solutions with specified numbers of simple generalized zeros for the nonlinear eigenvalue problem on time scales T−uΔΔ(t)+q(t)uσ(t)=rf(uσ(t)),t∈T,u(0)=u(1)=0, where r>0 is a given constant. In addition, we argue that our existence theorem is a generalization of a previous result which shows the existence of at least one positive solution for the above problem.