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Integro-differential equation of non-local wave interaction
Sbornik. Mathematics, Tome 198 (2007) no. 6, pp. 839-855 Cet article a éte moissonné depuis la source Math-Net.Ru

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The integro-differential equation $$ \frac{d^2f}{dx^2}+Af=\int^\infty_0K(x-t)f(t)\,dt+g(x) $$ with kernel $$ K(x)=\lambda\int^\infty_ae^{-|x|p}G(p)\,dp, \qquad a\geqslant0, $$ is considered, in which $$ A>0,\qquad \lambda\in(-\infty,\infty), \qquad G(p)\geqslant0, \qquad 2\int^\infty_a\frac1p\,G(p)\,dp=1. $$ These equations arise, in particular, in the theory of non-local wave interaction. A factorization method of their analysis and solution is developed. Bibliography: 9 titles. 
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N. B. Engibaryan; A. Kh. Khachatryan. Integro-differential equation of non-local wave interaction. Sbornik. Mathematics, Tome 198 (2007) no. 6, pp. 839-855. http://geodesic.mathdoc.fr/item/SM_2007_198_6_a4/

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