The determination in a certain domain $ D $
of variables $ x = ( x _ {1} \dots x _ {n} ) $
of a solution $ u( x) $
of a differential equation
$$ ( Lu ) ( x) = f ( x) ,\ x \in D , $$
from its values on (a part of) the boundary $ S $ of this domain:
$$ ( Bu ) ( y) = \phi ( y) ,\ y \in S , $$
where at least one of the operators $ L $ or $ B $ is non-linear.
See also Boundary value problem, ordinary differential equations; Boundary value problem, partial differential equations.
How to Cite This Entry:
Non-linear boundary value problem. Encyclopedia of Mathematics. URL: http://encyclopediaofmath.org/index.php?title=Non-linear_boundary_value_problem&oldid=47989
Non-linear boundary value problem. Encyclopedia of Mathematics. URL: http://encyclopediaofmath.org/index.php?title=Non-linear_boundary_value_problem&oldid=47989
This article was adapted from an original article by A.P. Soldatov (originator), which appeared in Encyclopedia of Mathematics - ISBN 1402006098. See original article