Construction of lower and upper solutions for first-order periodic problem

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• 作者：Ruyun Ma ; Lu Zhang
• 关键词：periodic boundary value problem ; singular problem ; lower and upper solutions
• 刊名：Boundary Value Problems
• 出版年：2015
• 出版时间：December 2015
• 年：2015
• 卷：2015
• 期：1
• 全文大小：1,522 KB
• 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 construct nonconstant lower and upper solutions for the periodic boundary value problem \(x'+f(t,x)=e(t)\), \(x(0)=x(T)\) and find their estimates. We prove the existence of positive solutions for the singular problem \(x'+g(x)=e(t)\), \(x(0)=x(T)\) by using these results.