Electronic Journal of Differential Equations,
Vol. 2011 (2011), No. 56, pp. 1-15.

Title: Fixed set theorems for discrete dynamics and nonlinear
       boundary-value problems
       
Authors: Robert Brooks  (Univ. of Utah, Salt Lake City, UT, USA)
         Klaus Schmitt  (Univ. of Utah, Salt Lake City, UT, USA)
	 Brandon Warner (Univ. of Utah, Salt Lake City, UT, USA)

Abstract:
 We consider self-mappings of  Hausdorff topological spaces which
 map compact sets to compact sets and establish the existence of
 invariant (fixed) sets. The fixed set results are used to provide
 fixed set analogues of well-known fixed point theorems. An
 algorithm is employed to compute the existence of fixed sets which
 are self-similar in a generalized sense. Some numerical examples
 are given. The utility of the abstract result is further
 illustrated via the study of a  boundary value problem for a
 system of differential equations

Submitted April 20, 2011. Published May 02, 2011.
Math Subject Classifications: 37B055, 37B10, 37L25, 34B15.
Key Words: Fixed sets; function system; self-similar sets;
    invariant sets;  Hausdorff metric; Hausdorff topology; 
    boundary value problem