Variable Change for Sturm-Liouville Differential Expression on Time Scales

We study second order scalar delta derivative expressions of Sturm-Liouville type on our newly defined Sturmian time scales. Sturmian time scales include the discrete and continuous cases studied by Sturm. A form of second order differential expression on a Sturmian time scale considered here satisfies a Green's identity and hence is"formally self-adjoint”. A unified variable change method is developed which allows simultaneous change of independent and dependent variable for expressions which include continuous and discrete theories as special cases. This unifies a continuous result of Coppel with a discrete result of Voepel. For the fourth order case, we explore unification of a continuous result of Ahlbrandt, Hinton and Lewis [4] with a discrete result of Voepel [32].