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A one-dimensional prescribed curvature equation modeling the corneal shape.

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We 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.

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Mean Curvature Equation Boundary Condition Positive Solution Existence Uniqueness Linear Stability Order Stability Lyapunov Stability Lower and Upper Solutions Monotone Approximation Topological Degree

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COELHO, Maria Isabel Esteves; CORSATO, Chiara; OMARI, Pierpaolo – A one-dimensional prescribed curvature equation modeling the corneal shape. Boundary Value Problems. ISSN: 1687-2770. Art. Nr. 127 (2014)

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Springer International Publishing AG

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