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∗The author was partially supported by Alexander von Humboldt Foundation and the Contract
MM-516 with the Bulgarian Ministry of Education, Science and Thechnology.
In this work we study the existence of global solution to
the semilinear wave equation (1.1) (∂2t − ∆)u = F(u),
where F(u) = O(|u|^λ) near |u| = 0 and λ > 1. Here and below ∆ denotes the Laplace
operator on R^n.
The existence of solutions with small initial data, for the case of space dimensions
n = 3 was studied by...
2000 Mathematics Subject Classification: 35C10, 35C20, 35P25, 47A40, 58D30, 81U40.
The Atkinson-Wilcox theorem claims that any scattered field
in the exterior of a sphere can be expanded into a uniformly and absolutely
convergent series in inverse powers of the radial variable and that once
the leading coefficient of the expansion is known the full series can be
recovered uniquely through a recurrence relation. The leading coefficient of
the series is known as the scattering amplitude...
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