Nonlinear Multi-Dimensional Continuous Integral Inequalities

Yuming Qin
Additional contact information
Yuming Qin: Donghua University, Department of Applied Mathematics College of Science

Chapter Chapter 5 in Integral and Discrete Inequalities and Their Applications, 2016, pp 535-764 from Springer

Abstract: Abstract The Pachpatte Inequality Assume that u(x,y),a(x,y),b(x,y) are non-negative continuous functions defined for all $$x,y \in \mathbb{R}_{+}$$ and $$F: \mathbb{R}_{+}^{3} \rightarrow \mathbb{R}_{+}$$ be a continuous function which satisfies the condition: for all u ≥ v ≥ 0, $$\displaystyle\begin{array}{rcl} & & 0 \leq F(x,y,u) - F(x,y,v) \leq K(x,y,v)(u - v), {}\\ \end{array}$$ where K(x,y,v) is a non-negative continuous function defined for all $$x,y,v \in \mathbb{R}_{+}$$ .

Keywords: Integral Inequalities; Pachpatte Inequalities; G Bond; Gronwall-Bellman Inequality; Characteristic Initial Value Problem (search for similar items in EconPapers)
Date: 2016
References: Add references at CitEc
Citations:

There are no downloads for this item, see the EconPapers FAQ for hints about obtaining it.

Related works:
This item may be available elsewhere in EconPapers: Search for items with the same title.

Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text

Persistent link: https://EconPapers.repec.org/RePEc:spr:sprchp:978-3-319-33304-5_5

Ordering information: This item can be ordered from
http://www.springer.com/9783319333045

DOI: 10.1007/978-3-319-33304-5_5

Access Statistics for this chapter

More chapters in Springer Books from Springer
Bibliographic data for series maintained by Sonal Shukla () and Springer Nature Abstracting and Indexing ().