Existence of Positive Solutions for Systems of Nonlinear Second-Order Differential Equations on the Half Line in a Banach Space
Received:November 23, 2009  Revised:January 19, 2010
Key Word: systems of singular differential equations   cone and ordering   positive solutions   M\"onch fixed point theorem   measure of non-compactness.  
Fund ProjectL:Supported by the National Natural Science Foundation of China (Grant No.10971179), the China Postdoctoral Science Foundation (Grant No.20110491154), the Foundation of Outstanding Middle-Aged and Young Scientists of Shandong Province (Grant No.BS2010SF004) and a Project of Shandong Province Higher Educational Science and Technology Program (Grant No.J10LA53).
Author NameAffiliation
Xing Qiu ZHANG School of Mathematics and Statistics, Huazhong University of Science and Technology, Hubei 430074, P. R. China
School of Mathematics, Liaocheng University, Shandong 252059, P. R. China 
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Abstract:
      In this paper, the cone theory and M\"onch fixed point theorem combined with the monotone iterative technique are used to investigate the positive solutions for a class of systems of nonlinear singular differential equations with multi-point boundary value conditions on the half line in a Banach space. The conditions for the existence of positive solutions are formulated. In addition, an explicit iterative approximation of the solution is also derived.
Citation:
DOI:10.3770/j.issn:1000-341X.2011.04.003
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