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Izv. RAN. Ser. Mat., 2010, Volume 74, Issue 5, Pages 191–204 (Mi izv4087)  

This article is cited in 6 scientific papers (total in 6 papers)

Solubility of a class of second-order integro-differential equations with monotone non-linearity on a semi-axis

Kh. A. Khachatryan

Institute of Mathematics, National Academy of Sciences of Armenia

Abstract: We consider a second-order integro-differential equation with locally monotone non-linearity and use special factorization methods to prove its solubility in the Sobolev space $W^2_\infty(0,+\infty)$. We also evaluate the limit of the solution at infinity in some cases.

Keywords: Sobolev space, iteration, monotonicity of a solution, Carathéodory condition.

DOI: https://doi.org/10.4213/im4087

Full text: PDF file (479 kB)
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English version:
Izvestiya: Mathematics, 2010, 74:5, 1069–1082

Bibliographic databases:

UDC: 517.968
MSC: Primary 47G20; Secondary 47H30
Received: 11.02.2009

Citation: Kh. A. Khachatryan, “Solubility of a class of second-order integro-differential equations with monotone non-linearity on a semi-axis”, Izv. RAN. Ser. Mat., 74:5 (2010), 191–204; Izv. Math., 74:5 (2010), 1069–1082

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  • https://doi.org/10.4213/im4087
  • http://mi.mathnet.ru/eng/izv/v74/i5/p191

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    Citing articles on Google Scholar: Russian citations, English citations
    Related articles on Google Scholar: Russian articles, English articles

    This publication is cited in the following articles:
    1. Kh. A. Khachatryan, “On solvability of one class high-order nonlinear integro-differential equations with Hammerstein type noncompact integral operator”, Ufa Math. J., 3:1 (2011), 101–110  mathnet  zmath
    2. Aref'eva I.Ya., Volovich I.V., “Cosmological daemon”, J. High Energ. Phys, 2011:8 (2011), 102  crossref  zmath  isi
    3. Kh. A. Khachatryan, “On a class of integral equations of Urysohn type with strong non-linearity”, Izv. Math., 76:1 (2012), 163–189  mathnet  crossref  crossref  mathscinet  zmath  adsnasa  isi  elib  elib
    4. Kh. A. Khachatryan, “Nontrivial solvability of a class of nonlinear integro-differential equations of second order”, Siberian Adv. Math., 23:4 (2013), 234–249  mathnet  crossref  mathscinet  elib
    5. N. B. Engibaryan, A. Kh. Khachatryan, “Solvability of an integrodifferential equation arising in the nonlocal interaction of waves”, Comput. Math. Math. Phys., 54:5 (2014), 834–844  mathnet  crossref  crossref  mathscinet  isi  elib  elib
    6. Kh. A. Khachatryan, H. S. Petrosyan, “One initial boundary-value problem for integro-differential equation of the second order with power nonlinearity”, Russian Math. (Iz. VUZ), 62:6 (2018), 43–55  mathnet  crossref  isi
  • Известия Российской академии наук. Серия математическая Izvestiya: Mathematics
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