Geodesic
Integro-differential equation of non-local wave interaction
Sbornik. Mathematics, Tome 198 (2007) no. 6, pp. 839-855 
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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     url = {http://geodesic.mathdoc.fr/item/SM_2007_198_6_a4/}
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Voir la notice de l'article provenant de la source Math-Net.Ru

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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[7] N. B. Engibaryan, B. N. Engibaryan, “Integralnoe uravnenie svertki na polupryamoi s vpolne monotonnym yadrom”, Matem. sb., 187:10 (1996), 53–72 | MR | Zbl

[8] M. G. Krein, Yu. L. Shmulyan, “Uravneniya Vinera–Khopfa, yadra kotorykh dopuskayut integralnoe predstavlenie cherez eksponenty, I, II”, Izv. AN ArmSSR. Matem., 17:4 (1982), 307–327 | MR | Zbl

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