The Leray-Schauder Principle and Applications

Radu Precup
Additional contact information
Radu Precup: Babeş-Bolyai University, Department of Applied Mathematics

Chapter Chapter 4 in Methods in Nonlinear Integral Equations, 2002, pp 43-60 from Springer

Abstract: Abstract In applications one of the drawbacks of Schauder’s fixed point theorem is the invariance condition T (D) ⊂ D which has to be guaranteed for a bounded closed convex subset D of a Banach space. The Leray-Schauder principle [32] makes it possible to avoid such a condition and requires instead that a ‘boundary condition’ is satisfied. In this chapter we shall prove the Leray-Schauder principle and we shall apply it in order to obtain existence results for continuous solutions of integral equations. In particular, we give results on the existence of continuous solutions of initial value and two-point boundary value problems for nonlinear ordinary differential equations in R n . The results will be better than those established by means of Schauder’s theorem.

Date: 2002
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:978-94-015-9986-3_5

Ordering information: This item can be ordered from
http://www.springer.com/9789401599863

DOI: 10.1007/978-94-015-9986-3_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 ().