Author:
Coelho Isabel,Corsato Chiara,Omari Pierpaolo
Abstract
Abstract
We prove existence, uniqueness, and stability of solutions of the prescribed curvature problem
(
u
′
/
1
+
u
′
2
)
′
=
a
u
−
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.
Publisher
Springer Science and Business Media LLC
Subject
Algebra and Number Theory,Analysis
Cited by
11 articles.
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