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Non-linear boundary value problem

From Encyclopedia of Mathematics
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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
This article was adapted from an original article by A.P. Soldatov (originator), which appeared in Encyclopedia of Mathematics - ISBN 1402006098. See original article