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A nonlinear mathematical model of the corneal shape. (English) Zbl 1239.34004
Summary: We consider a nonlinear two-point boundary value problem which is derived as a description of corneal shape. We prove some basic results concerning existence, uniqueness and estimates. We suggest some approximate solution fitting over fifteen thousands real corneal data points with an error of order of 1%.

MSC:
34A05 Explicit solutions, first integrals of ordinary differential equations
37N25 Dynamical systems in biology
92C05 Biophysics
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