A one-dimensional prescribed curvature equation modeling the corneal shape

DOI10.1186/1687-2770-2014-127zbMath1307.34043OpenAlexW2146275305WikidataQ59395308 ScholiaQ59395308MaRDI QIDQ476954

Chiara Corsato, Pierpaolo Omari, Isabel Coelho

Publication date: 2 December 2014

Published in: Boundary Value Problems (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1186/1687-2770-2014-127

zbMATH Keywords

lower and upper solutionslinear stabilityLyapunov stabilitymonotone approximationmixed boundary conditionorder stability

Mathematics Subject Classification ID

Nonlinear boundary value problems for ordinary differential equations (34B15) Theoretical approximation of solutions to ordinary differential equations (34A45) Applications of operator theory to differential and integral equations (47N20) Parameter dependent boundary value problems for ordinary differential equations (34B08)

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The Dirichlet problem for a prescribed anisotropic mean curvature equation: existence, uniqueness and regularity of solutions ⋮ A prescribed anisotropic mean curvature equation modeling the corneal shape: a paradigm of nonlinear analysis ⋮ Radial solutions of the Dirichlet problem for a class of quasilinear elliptic equations arising in optometry ⋮ A highly accurate matrix method for solving a class of strongly nonlinear BVP arising in modeling of human shape corneal ⋮ Solution estimates for a system of nonlinear integral equations arising in optometry ⋮ Numerical solution of nonlinear integral equation arising in optometry ⋮ Radially symmetric solutions of an anisotropic mean curvature equation modeling the corneal shape

Cites Work

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• A nonlinear mathematical model of the corneal shape
• Existence and multiplicity results for the prescribed mean curvature equation via lower and upper solutions.
• Bessel function model of corneal topography
• A constructive monotone iterative method for second-order BVP in the presence of lower and upper solutions
• Existence, regularity and stability properties of periodic solutions of a capillarity equation in the presence of lower and upper solutions
• On a nonlinear boundary value problem modeling corneal shape
• Two-point boundary value problems. Lower and upper solutions
• On a sub-supersolution method for the prescribed mean curvature problem
• Regularization of an ill-posed problem in corneal topography