On Green's functions and positive solutions for boundary value problems on time scales

Authors:
F. Merdivenci Atici;G. Sh. Guseinov
Affiliations:
Department of Mathematics, Ege University, 35100 Bornova, Izmir, Turkey;Department of Mathematics, Ege University, 35100 Bornova, Izmir, Turkey
Venue:
Journal of Computational and Applied Mathematics - Dynamic equations on time scales
Year:
2002

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Abstract

In this paper we offer a form of self-adjoint differential equations on time scales so that the associated Green's function is found symmetric in the usual sense. For this purpose together with the delta derivative we employ the nabla derivative as well. We introduce the concepts of Lebesgue delta and nabla integrals on time scales. Next, sign properties of the Green's function are investigated and existence results for positive solutions of nonlinear boundary value problems are established. Upper and lower bounds for these positive solutions also are given.