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Advisor(s)
Abstract(s)
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.
Description
Keywords
Mean Curvature Equation Boundary Condition Positive Solution Existence Uniqueness Linear Stability Order Stability Lyapunov Stability Lower and Upper Solutions Monotone Approximation Topological Degree
Citation
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)
Publisher
Springer International Publishing AG