Singular multiparameter dynamic equations with distributional potentials on time scales

Abstract

In this paper, we consider both singular single and several multiparameter second order dynamic equations with distributional potentials on semi-innite time scales. At rst we construct Weyl's theory for the single singular multiparameter dynamic equation with  distributional potentials and we prove that the forward jump of at least one solution of this equation must be squarely integrable with respect to some multiple function which is of one sign and nonzero on the given time scale. Then using the obtained results for the single dynamic equation with several parameters, we investigate the number of the products of the squarely integrable solutions of the singular several equations with  distributional potentials and several parameters.

Mathematics Subject Classication (2010): 34B20, 34B24, 34B05, 34B40, 34N05.

Key words: Dynamic equation, multiparameter eigenvalue problem, Weyl theory, distributional potential, time scales.