Tuyển tập báo cáo các nghiên cứu khoa học quốc tế ngành hóa học dành cho các bạn yêu hóa học tham khảo đề tài: Research Article Existence and Uniqueness of Positive Solution for Singular BVPs on Time Scales | Hindawi Publishing Corporation Advances in Difference Equations Volume 2009 Article ID 728484 12 pages doi 2009 728484 Research Article Existence and Uniqueness of Positive Solution for Singular BVPs on Time Scales Ana Gomez Gonzalez1 and Victoria Otero-Espinar2 1 Departamento de Matematica Aplicada Facultade de Matematicas Universidade de Santiago de Compostela 15782 Galicia Spain 2 Departamento de Analise Matemdtica Facultade de Matemdticas Universidade de Santiago de Compostela 15782 Galicia Spain Correspondence should be addressed to Victoria Otero-Espinar Received 27 March 2009 Accepted 12 May 2009 Recommended by Alberto Cabada This paper is devoted to derive some sufficient conditions for the existence and uniqueness of positive solutions to a singular second-order dynamic equation with Dirichlet boundary conditions. Copyright 2009 A. Gomez Gonzalez and V. Otero-Espinar. This is an open access article distributed under the Creative Commons Attribution License which permits unrestricted use distribution and reproduction in any medium provided the original work is properly cited. 1. Introduction Hilger 1 introduced the notion of time scale in 1990 in order to unify the theory of continuous and discrete calculus. The field of dynamic equations on time scale contains links and extends the classical theory of differential and difference equations besides many others. There are more time scales than just R corresponding to the continuous case and N discrete case and hence many more classes of dynamic equations. By time scale we mean a closed subset of the real numbers. Let T be an arbitrary time scale. We assume that T has the topology that it inherits from the standard topology on R. Assume that a b are points in T and define the time scale interval a b T t e T a t b . For t e T define the forward jump operator ơ T T by ơ t inf s e T s t and the backward jump operator p T T by p t sup s e T s t . In this definition we put ơ t t if T
