Positive Solution to a Singular p-Laplacian BVP with Sign-Changing Nonlinearity Involving Derivative on Time Scales

Abstract

Let T be a time scale such that 0,T∈T. By using a monotone iterative method, we present some existence criteria for positive solution of a multiple point general Dirichlet-Robin BVP on time scales with the singular sign-changing nonlinearity. These results are even new for the corresponding differential (T=ℝ) and difference equation (T=ℤ) as well as in general time scales setting. As an application, an example is given to illustrate the results. The interesting point here is that the sign-changing nonlinear term is involved with the first-order derivative explicitly, and the singularity may occur at u=0, t=0, and t=T.