Electron. J. Diff. Equ., Vol. 2013 (2013), No. 02, pp. 1-16.

Notes on expansive mappings and a partial answer to Nirenberg's problem

Tian Xiang

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 7, 2013.
Math Subject Classifications: 58C05, 47H05, 47H10.
Key Words: Expansive mapping; fixed point; Monotone operator; Nirenberg's problem.

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Tian Xiang
Department of Mathematics
Tulane University
New Orleans, LA 70118, USA
email: txiang@tulane.edu

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