A one-dimensional prescribed curvature equation modeling the corneal shape

We prove existence, uniqueness, and stability of solutions of the prescribed curvature problem (u′/1+u′2)′=au−b/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 (Okrasiński and Płociniczak 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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