Solvability for system of nonlinear singular differential equations with integral boundary conditions

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• 作者：Yaohong Li (1)
  Haiyan Zhang (1)
  
  1. School of Mathematics and Statistics ; Suzhou University ; Suzhou ; Anhui ; 234000 ; P.R. China
  
• 关键词：34B16 ; 34B18 ; positive solutions ; integral boundary conditions ; higher ; order differential equations ; fixed point theorem
• 刊名：Boundary Value Problems
• 出版年：2014
• 出版时间：December 2014
• 年：2014
• 卷：2014
• 期：1
• 全文大小：1,224 KB
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• 刊物主题：Difference and Functional Equations; Ordinary Differential Equations; Partial Differential Equations; Analysis; Approximations and Expansions; Mathematics, general;
• 出版者：Springer International Publishing
• ISSN：1687-2770

文摘

By using the Banach contraction principle and the Leggett-Williams fixed point theorem, this paper investigates the uniqueness and existence of at least three positive solutions for a system of mixed higher-order nonlinear singular differential equations with integral boundary conditions: $$\left \{ \begin{array}{l} u^{(n_{1})}(t)+a_{1}(t)f_{1}(t, u(t), v(t))=0,\quad 0 where the nonlinear terms \(f_{i}\) , \(g_{i}\) satisfy some growth conditions, \(\beta_{i}[\cdot]\) are linear functionals given by \(\beta_{i}[w]=\int^{1}_{0}w(s)\,\mathrm{d}\phi_{i}(s)\) , involving Stieltjes integrals with positive measures, and \(i=1, 2\) . We give an example to illustrate our result.