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oai:docta.ucm.es:20.500.14352/338762024-07-19T15:23:18Zcom_20.500.14352_14col_20.500.14352_15

On a nonlinear boundary value problem modeling corneal shape Płociniczak, Łukasz Okrasinski, W. Nieto, J. J. Domínguez Bonilla, Óscar 517 Boundary-value problem Corneal topography Estimates Análisis matemático 1202 Análisis y Análisis Funcional 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 Polish Government Ministerio de Economía, Comercio y Empresa (España) Fondo Europeo de Desarrollo Regional Depto. de Análisis Matemático y Matemática Aplicada Fac. de Ciencias Matemáticas TRUE pub 2023-06-19T13:30:00Z 2023-06-19T13:30:00Z 2014-06 journal article https://hdl.handle.net/20.500.14352/33876 0022-247X 7dx.doi.org/10.1016/j.jmaa.2014.01.010 eng NCN 2012/05/N/ST1/02860 MTM2010-15314 MTM2010-15814 FPU grant AP2012-0779 Płociniczak, Ł., Okrasinski, W., Nieto, J. J. & Domínguez Bonilla, Ó. «On a Nonlinear Boundary Value Problem Modeling Corneal Shape». Journal of Mathematical Analysis and Applications, vol. 414, n.o 1, junio de 2014, pp. 461-71. DOI.org (Crossref), https://doi.org/10.1016/j.jmaa.2014.01.010. restricted access application/pdf Elsevier