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  with a discrete result of Voepel .
C. D. Ahlbrandt et al., "Variable Change for Sturm-Liouville Differential Expression on Time Scales," Journal of Difference Equations and Applications, Taylor & Francis, Jan 2003.
The definitive version is available at https://doi.org/10.1080/10236100309487537
Mathematics and Statistics
Keywords and Phrases
Sturm-Liouvill equations; Time scales; Delta derivatives; variable change
Article - Journal
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