On a nonlinear boundary value problem modeling corneal shape

JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS

卷:414

Article

Plociniczak, Lukasz¹  Okrasinski, Wojciech¹  Nieto, Juan J.^2,3  Dominguez, Oscar⁴ 

[1] Wroclaw Univ Technol, Inst Math & Comp Sci, PL-50372 Wroclaw, Poland

[2] Univ Santiago de Compostela, Dept Anal Matemat, Santiago De Compostela 15782, Spain

[3] King Abdulaziz Univ, Dept Math, Fac Sci, Jeddah 21589, Saudi Arabia

[4] Univ Complutense Madrid, Fac Matemat, Dept Anal Matemat, E-28040 Madrid, Spain

关键词: Boundary-value problem;    Corneal topography;    Estimates;   

DOI  :  10.1016/j.jmaa.2014.01.010

来源: Elsevier

【 摘 要 】

In this paper we present some results concerning a boundary value problem for a nonlinear ordinary differential equation that was used before in modeling the topography of human cornea. These results generalize previously obtained theorems on existence and uniqueness. We show that our equation has a unique solution for all parameters and conditions that, can arise in physical situation. In the second part of the article we derive some new estimates and approximate solutions. Numerical calculations verify that these approximations are very accurate. (C) 2014 Elsevier Inc. All rights reserved.

【 授权许可】

Free