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On the Newton principle for the Helmholtz equation

The Helmholtz equation with a compactly supported source f(x) localized in the ball V A = {|x| ≤ A} and with the Sommerfeld condition at infinity is considered on the entire space R n . A singular source T(x) (with support localized at the point {x = 0}) is constructed, such that solutions to the original problem and to the Newton problem are identical in R n | V A . The well-posedness of the Newton problem is proved in the class of analytic functionals Z'(R n ).