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



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 


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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

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