The authors prove an existence and uniqueness result for the nonlinear boundary value problem on a time scale
with Dirichlet conditions and certain sign and growth conditions on the nonlinearity . The symbols and are notions from time scales calculus. A time scale is an arbitrary closed subset of the reals. The result shows that there is a curve of solutions, parameterized by , being the principal eigenvalue of an associated weighted eigenvalue problem. The main ingredients of the proof are a fixed-point theorem in a cone, maximum principle and generalizations of known techniques to the time scales case.