Unformatted text preview: 38 1 Solutions 8. The corresponding integral equation is We now have 9. The corresponding integral equation is We then have 10. The right hand side is
. Then
. Both and
are continuous in the whole
plane and thus are continuous on
any rectangle containing the origin
. Picard’s theorem applies and
we can conclude there is a unique solution on an interval about .
11. The right hand side is
. If
is any rectangle about
then there are coordinates that are negative. Hence is not deﬁned on
and Picards’ theorem does not apply. ...
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 Fall '08
 BELL,D
 corresponding integral equation

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