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 Multipoint Singular Boundary-Value Problem for Systems of Nonlinear Differential Equations | Hindawi Publishing Corporation Boundary Value Problems Volume 2009 Article ID 137451 20 pages doi 2009 137451 Research Article Multipoint Singular Boundary-Value Problem for Systems of Nonlinear Differential Equations Jaromír BaStinec 1 Josef Diblik 1 2 and Zdenek Smarda1 1 Department of Mathematics Faculty of Electrical Engineering and Communication Brno University of Technology Technicka 8 616 00 Brno Czech Republic 2 Department of Mathematics and Descriptive Geometry Faculty of Civil Engineering Brno University of Technology Zizkova 17 662 37 Brno Czech Republic Correspondence should be addressed to Josef Diblik Received 14 April 2009 Revised 9 July 2009 Accepted 16 August 2009 Recommended by Donal O Regan A singular Cauchy-Nicoletti problem for a system of nonlinear ordinary differential equations is considered. With the aid of combination of Wazewski s topological method and Schauder s principle the theorem concerning the existence of a solution of this problem having the graph in a prescribed domain is proved. Copyright 2009 Jaromír Bastinec 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 In the present paper the following Cauchy-Nicoletti problem y i fi x y i 1 . n yp xp Ap yq xq Aq yr xr Ar p 1 . k q k 1 . s r s 1 . n is considered where y y1 . yn x e I a b and a x1 xk xk 1 xs xs 1 xn b Ai i 1 . n are real constants. Denote Ii I xi i 1 . n and J n 1Ii. We will suppose fi e C i R i 1 . n where the domain 0i c Ii X Rn satisfying a relation 0in x x f 0 for every x e If is more precisely specified in Section 2. The continuity of the function fi is not required at the point xi i 1 . n. Solution of the problem is defined in the following sense. 2 Boundary Value Problems Definition . A vector-function y x yi x . yn x e C I R with yi
