Electronic Journal of Differential Equations,
Vol. 2013 (2013), No. 02, pp. 1-16.

Title: Notes on expansive mappings and a partial answer
       to Nirenberg's problem
        
Author: Tian Xiang (Tulane Univ., New Orleans, LA, USA)

Abstract: 
 In this article, two minor flaws made in the preceding paper [19]
 are corrected. And then several remarks concerning expansive mappings and
 their connection with monotone operators are observed.
 These observations are then used for generalizing the  Minty-Browder theorem
 [9,2] and  further answer to Nirenberg's open question.
 Along this lines, a strengthened Nirenberg's problem is formulated and
 a surjective result for expansive mappings is obtained.
 Finally, two interesting conjectures concerning ``reverse" Schauder
 fixed point theorem are raised.

Submitted May 22, 2012. Published January 07, 2013.
Math Subject Classifications: 58C05, 47H05, 47H10.
Key Words: Expansive mapping; fixed point; Monotone operator; 
           Nirenberg's problem.