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 Multiple Positive Solutions in the Sense of Distributions of Singular BVPs on Time Scales and an Application to Emden-Fowler Equations | Hindawi Publishing Corporation Advances in Difference Equations Volume 2008 Article ID 796851 13 pages doi 2008 796851 Research Article Multiple Positive Solutions in the Sense of Distributions of Singular BVPs on Time Scales and an Application to Emden-Fowler Equations Ravi P. Agarwal 1 Victoria Otero-Espinar 2 Kanishka Perera 1 and Dolores R. Vivero2 1 Department of Mathematical Sciences Florida Institute of Technology Melbourne FL 32901 USA 2 Departamento de Analise Matemdtica Facultade de Matemdticas Universidade de Santiago de Compostela 15782 Santiago de Compostela Galicia Spain Correspondence should be addressed to Ravi P. Agarwal agarwal@ Received 21 April 2008 Accepted 17 August 2008 Recommended by Paul Eloe This paper is devoted to using perturbation and variational techniques to derive some sufficient conditions for the existence of multiple positive solutions in the sense of distributions to a singular second-order dynamic equation with homogeneous Dirichlet boundary conditions which includes those problems related to the negative exponent Emden-Fowler equation. Copyright 2008 Ravi P. Agarwal et al. 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 The Emden-Fowler equation uAA t q f ua ơ f 0 t e 0 1 T arises in the study of gas dynamics and fluids mechanics and in the study of relativistic mechanics nuclear physics and chemically reacting system see . 1 and the references therein for the continuous model. The negative exponent Emden-Fowler equation a 0 has been used in modeling non-Newtonian fluids such as coal slurries 2 . The physical interest lies in the existence of positive solutions. We are interested in a broad class of singular problem that includes those related with and the more general equation wAA t q f ua ơ t g t uơ t t e 0 1 T. .
