Journal of Mathematical Sciences

, Volume 181, Issue 1, pp 65–77 | Cite as

On the solvability of a nonlinear second-order integro-differential equation with sum-difference kernel on a semiaxis

  • Khachatur A. Khachatryan
  • Mikael G. Kostanyan


We consider a class of nonlinear second-order integro-differential equations with sum-difference kernel on a positive semiaxis. By constructing a special factorization of the initial linear integro-differential operator, we prove the existence of a nonnegative, nontrivial, and monotonically increasing solution and determine its asymptotic behavior at infinity. The relevant examples are presented.


Factorization eigenvalue limit of a solution successive approximations Sobolev space 


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.



  1. 1.
    L. G. Arabadzhyan and N. B. Engibaryan, “Equations in convolutions and nonlinear functional equations,” in: Totals of Science and Technique. Mathematical Analysis [in Russian], VINITI, Moscow, 1984, pp. 175–242.Google Scholar
  2. 2.
    N. B. Engibaryan and L. G. Arabadzhyan, “On some problems of factorization for integral operators of the convolution type,” Diff. Uravn., 26, No. 1, 1442–1452 (1990).MathSciNetMATHGoogle Scholar
  3. 3.
    Kh. A. Khachatryan, “Solvability of a class of second-order integro-differential equations with monotonic nonlinearity on a semiaxis,” Izv. RAN. Ser. Mat., 74, No. 5, 191–204 (2010).MathSciNetGoogle Scholar
  4. 4.
    Kh. A. Khachatryan and E. A. Khachatryan, “On the solvability of some classes of nonlinear integro-differential equations with noncompact operator,” Izv. VUZ. Mat., KGU, 54, No. 1, 91–100 (2011).MathSciNetGoogle Scholar
  5. 5.
    A. N. Kolmogorov and S. V. Fomin, Elements of the Theory of Functions and Functional Analysis, Dover, New York, 1999.Google Scholar
  6. 6.
    M. A. Krasnoselskii, P. P. Zabreiko, E. I. Pustylnik, and P. E. Sobolevskii, Integral Operators in Spaces of Summable Functions, Noordhoff, Leiden, 1976.CrossRefGoogle Scholar
  7. 7.
    L. D. Landau and E. M. Lifshitz, Quantum Mechanics. Non-Relativistic Theory, Pergamon Press, New York, 1980.Google Scholar

Copyright information

© Springer Science+Business Media, Inc. 2012

Authors and Affiliations

  • Khachatur A. Khachatryan
    • 1
  • Mikael G. Kostanyan
    • 2
  1. 1.Institute of Mathematics of the NAN of RAErevanRepublic of Armenia
  2. 2.Armenian State Agrarian UniversityErevanRepublic of Armenia

Personalised recommendations