Boundary Value Problems on Infinite Intervals: A Topological Approach

Ravi Agarwal (), Martin Bohner () and Donal O’Regan ()
Additional contact information
Ravi Agarwal: Florida Institute of Technology, Department of Mathematical Sciences
Martin Bohner: Florida Institute of Technology, Department of Mathematical Sciences
Donal O’Regan: National University of Ireland, Department of Mathematics

Chapter Chapter 9 in Advances in Dynamic Equations on Time Scales, 2003, pp 275-291 from Springer

Abstract: Abstract The aim of this chapter is twofold. First we wish to survey most of the fixed point theorems available in the literature for compact operators defined on Fréchet spaces. In particular we present the three “most applicable” results from the literature in Section 9.2. The first result is the well-known Schauder-Tychonoff theorem, the second, a Furi-Pera type result and the third, a fixed point result based on a diagonalization argument. Applications of these fixed point theorems to differential and difference equations can be found in a recent book of Agarwal and O’Regan [17]. Our second aim is to survey the results in the literature concerning time scale problems on infinite intervals. Only a handful of results are known, and the theory we present in Section 9.3 is based on the diagonalization approach in Section 9.2; this approach seems to give the most general and natural results. In Section 9.4 we consider linear systems on infinite intervals.

Keywords: Convex Subset; Fixed Point Problem; Infinite Interval; Frechet Space; Nonlinear Alternative (search for similar items in EconPapers)
Date: 2003
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:978-0-8176-8230-9_9

Ordering information: This item can be ordered from
http://www.springer.com/9780817682309

DOI: 10.1007/978-0-8176-8230-9_9

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 ().