Eigenvalue problems for higher-order p-Laplacian dynamic equations on time scales

Let T be a time scale. The existence of positive solutions for the nonlinear four-point singular boundary value eigenvalue problem with higher-order p-Laplacian dynamic equations on time scales is studied. By using the fixed-point index theory, we derive an explicit interval of λ such that for any λ in this interval, the existence of at least one positive solution to the eigenvalue problem is guaranteed, and the existence of at least two solutions for λ in an appropriate interval is also discussed.