Coelho, Maria Isabel EstevesCorsato, ChiaraOmari, Pierpaolo2015-05-142015-05-142014-05COELHO, Maria Isabel Esteves; CORSATO, Chiara; OMARI, Pierpaolo - A one-dimensional prescribed curvature equation modeling the corneal shape. Boundary Value Problems. (2014)1687-2770http://hdl.handle.net/10400.21/4536We prove existence, uniqueness, and stability of solutions of the prescribed curvature problem (u'/root 1 + u'(2))' = au - b/root 1 + u'(2) in [0, 1], u'(0) = u(1) = 0, for any given a > 0 and b > 0. We also develop a linear monotone iterative scheme for approximating the solution. This equation has been proposed as a model of the corneal shape in the recent paper (Okrasinski and Plociniczak in Nonlinear Anal., Real World Appl. 13:1498-1505, 2012), where a simplified version obtained by partial linearization has been investigated.engMean curvature equationMixed boundary conditionPositive solutionExistenceUniquenessLinear stabilityOrder stabilityLyapunov stabilityLower and upper solutionsMonotone approximationTopological degreejournal article10.1186/1687-2770-2014-127