Tuyển tập các báo cáo nghiên cứu về sinh học được đăng trên tạp chí sinh học Journal of Biology đề tài: Research Article Analysis and Numerical Solutions of Positive and Dead Core Solutions of Singular Sturm-Liouville Problems | Hindawi Publishing Corporation Advances in Difference Equations Volume 2010 Article ID 969536 37 pages doi 2010 969536 Research Article Analysis and Numerical Solutions of Positive and Dead Core Solutions of Singular Sturm-Liouville Problems Gernot Pulverer 1 Svatoslav Stanek 2 and Ewa B. Weinmuller1 1 Institute for Analysis and Scientific Computing Vienna University of Technology Wiedner Hauptstrasse 6-10 1040 Vienna Austria 2 Department of Mathematical Analysis Faculty of Science Palacky University Tomkova 40 779 00 Olomouc Czech Republic Correspondence should be addressed to Svatoslav Stanek stanek@ Received 20 December 2009 Accepted 28 April 2010 Academic Editor Josef Diblik Copyright 2010 Gernot Pulverer 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. In this paper we investigate the singular Sturm-Liouville problem u Xg u u 0 0 fiu d au 1 A where A. is a nonnegative parameter f 0 a 0 and A 0. We discuss the existence of multiple positive solutions and show that for certain values of X- there also exist solutions that vanish on a subinterval 0 p c 0 1 the so-called dead core solutions. The theoretical findings are illustrated by computational experiments for g u 1 ựũ and for some model problems from the class of singular differential equations f u f t u Xg t u u discussed in Agarwal et al. 2007 . For the numerical simulation the collocation method implemented in our MATLAB code bvpsuite has been applied. 1. Introduction In the theory of diffusion and reaction see . 1 the reaction-diffusion phenomena are described by the equation Av ộ2h x v where x Q c RN. Here v 0 is the concentration of one of the reactants and Ộ is the Thiele modulus. In case that h is radial symmetric with respect to x the radial solutions of the above 2 Advances in Difference Equations equation .
