Electron. J. Diff. Equ., Vol. 2011 (2011), No. 42, pp. 1-11.

Operator type expansion-compression fixed point theorem

Douglas R. Anderson, Richard I. Avery, Johnny Henderson, Xueyan Liu

This article presents an alternative to the compression and expansion fixed point theorems of functional type by using operators and functions to replace the functionals and constants that are used in functional compression and expansion fixed point theorems. Only portions of the boundaries are required to be mapped outward or inward in the spirit of the original work of Leggett-Williams. We conclude with an application verifying the existence of a positive solution to a second-order boundary-value problem.

Submitted October 27, 2010. Published March 25, 2011.
Math Subject Classifications: 47H10.
Key Words: Fixed-point theorems; Leggett-Williams; expansion; compression; positive solutions.

Show me the PDF file (226 KB), TEX file, and other files for this article.

Douglas R. Anderson
Department of Mathematics and Computer Science
Concordia College, Moorhead, MN 56562, USA
email: andersod@cord.edu
Richard I. Avery
College of Arts and Sciences, Dakota State University
Madison, South Dakota 57042, USA
email: rich.avery@dsu.edu
Johnny Henderson
Department of Mathematics, Baylor University
Waco, TX 76798, USA
email: Johnny_Henderson@baylor.edu
Xueyan (Sherry) Liu
Department of Mathematics, Baylor University
Waco, TX 76798-7328, USA
email: Xueyan_Liu@baylor.edu

Return to the EJDE web page