Solvability of nth-order Lipschitz equations with nonlinear three-point boundary conditions

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• 作者：Minghe Pei (1)
  Sung Kag Chang (2)
  
  1. Department of Mathematics ; Beihua University ; JiLin ; 132013 ; People鈥檚 Republic of China
  2. Department of Mathematics ; Yeungnam University ; Kyongsan ; 712-749 ; Korea
  
• 关键词：34B10 ; 34B15 ; nth ; order Lipschitz equation ; nonlinear three ; point boundary value problem ; matching method ; existence ; uniqueness
• 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：1,299 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

In this paper, we investigate the solvability of nth-order Lipschitz equations \(y^{(n)}=f(x,y,y',\ldots,y^{(n-1)})\) , \(x_{1}\leq x\leq x_{3}\) , with nonlinear three-point boundary conditions of the form \(k(y(x_{2}),y'(x_{2}),\ldots,y^{(n-1)}(x_{2});y(x_{1}),y'(x_{1}),\ldots ,y^{(n-1)}(x_{1}))=0\) , \(g_{i}(y^{(i)}(x_{2}),y^{(i+1)}(x_{2}),\ldots,y^{(n-1)}(x_{2}))=0\) , \(i=0,1,\ldots,n-3\) , \(h(y(x_{2}),y'(x_{2}),\ldots,y^{(n-1)}(x_{2}); y(x_{3}),y'(x_{3}),\ldots ,y^{(n-1)}(x_{3}))=0\) , where \(n\geq3\) , \(x_{1} . By using the matching technique together with set-valued function theory, the existence and uniqueness of solutions for the problems are obtained. Meanwhile, as an application of our results, an example is given.