Geodesic
One initial boundary-value problem for integro-differential equation of the second order with power nonlinearity
Izvestiâ vysših učebnyh zavedenij. Matematika, no. 6 (2018), pp. 48-62.

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In the Sobolev space $W_\infty^2(\mathbb{R}^+)$ we investigate one initial boundary-value problem for integro-differential equation of the second order with power nonlinearity on a semi-axis. Assuming that summary-difference even kernel serves for the considered kernel as minorant in the sense of M.A. Krasnosel'skii, we prove the existence of nonnegative (nontrivial) solution in the Sobolev space $W_\infty^2(\mathbb{R}^+)$. We also calculate the limits of constructed solution at the infinity.
Mots-clés : nonnegative solution
Keywords: iteration, limit of solution, Sobolev space, monotonicity. 
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     title = {One initial boundary-value problem for integro-differential equation of the second order with power nonlinearity},
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Kh. A. Khachatryan; H. S. Petrosyan. One initial boundary-value problem for integro-differential equation of the second order with power nonlinearity. Izvestiâ vysših učebnyh zavedenij. Matematika, no. 6 (2018), pp. 48-62. http://geodesic.mathdoc.fr/item/IVM_2018_6_a4/

[1] Kasti Dzh., Kalaba R., Metody pogruzheniya v prikladnoi matematike, Mir, M., 1976

[2] Baraff G. A., “Transmission of electromagnetic waves through a conducting slab. I. The two-sided Wiener–Hopf solution”, J. Math. Phys., 9:3 (1968), 372–384 | DOI | MR

[3] Engibaryan N. B., Khachatryan A. Kh., “Integro-differentsialnoe uravnenie nelokalnogo vzaimodeistviya voln”, Matem. sb., 198:6 (2007), 89–106 | DOI

[4] Engibaryan N. B., Khachatryan A. Kh., “O razreshimosti integro-differentsialnogo uravneniya, voznikayuschego v zadache o nelokalnom vzaimodeistvii voln”, Zhurn. vychisl. matem. i matem. fiz., 54:5 (2014), 834–844 | DOI | MR

[5] Khachatryan Kh. A., “Razreshimost odnogo klassa integro-differentsialnykh uravnenii vtorogo poryadka s monotonnoi nelineinostyu na poluosi”, Izv. RAN. Ser. matem., 74:5 (2010), 191–204 | DOI | MR

[6] Khachatryan Kh. A., “O netrivialnoi razreshimosti odnogo klassa nelineinykh integro-differentsialnykh uravnenii vtorogo poryadka”, Matem. tr., 15:2 (2012), 172–193

[7] Khachatryan Kh. A., “Postroenie netrivialnogo resheniya odnoi sistemy nelineinykh integro-differentsialnykh uravnenii”, Izv. NAN Armenii. Matem., 45:2 (2010), 67–76 | MR

[8] Kolmogorov A. N., Fomin V. S., Elementy teorii funktsii i funktsionalnogo analiza, M., 1981

[9] Arabadzhyan L. G., Engibaryan N. B., “Uravneniya v svertkakh i nelineinye funktsionalnye uravneniya”, Itogi nauki i tekhn. Matem. analiz, 22, 1984, 175–242

[10] Budak B. M., Fomin S. V., Kratnye integraly i ryady, Fizmatlit, M., 1965

[11] Engibaryan N. B., “Uravneniya vosstanovleniya na poluosi”, Izv. RAN. Ser. matem., 63:1 (1999), 61–76 | DOI