Principal solution in Weyl-Titchmarsh theory for second order Sturm-Liouville equation on time scales

A connection between the oscillation theory and theWeyl--Titchmarsh theory for the second order Sturm--Liouvilleequation on time scales is established by using the principalsolution. In particular, it is shown that the Weyl solutioncoincides with the principal solution in the limit point case,and consequently the square integrability of the Weyl solutionis obtained. Moreover, both limit point and oscillatorycriteria are derived in the case of real-valued coefficients,while a~generalization of the invariance of the limit circlecase is proven for complex-valued coefficients. Several ofthese results are new even in the discrete time case. Finally,some illustrative examples are provided.