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Mat. Sb. (N.S.), 1975, Volume 97(139), Number 1(5), Pages 35–58 (Mi msb3480)  

This article is cited in 23 scientific papers (total in 23 papers)

Integral equations on the half-line with difference kernels and nonlinear functional equatons

N. B. Engibaryan, A. A. Arutyunyan

Abstract: In this paper we present a new approach to the solution of scalar and operator equations of the form
\begin{equation*} f(x)=g(x)+\int_0^\infty T(x-t)f(t) dt. \tag{A} \end{equation*}

We derive and study some new functional equations, occupying an intermediate position between the equation (A) and the Ambarcumyan equation. This approach leads to a very simple way of deriving and generalizing Ambarcumyan's equations.
Bibliography: 18 titles.

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English version:
Mathematics of the USSR-Sbornik, 1975, 26:1, 31–54

Bibliographic databases:

UDC: 517.948
MSC: Primary 45E10; Secondary 47G05
Received: 05.03.1974

Citation: N. B. Engibaryan, A. A. Arutyunyan, “Integral equations on the half-line with difference kernels and nonlinear functional equatons”, Mat. Sb. (N.S.), 97(139):1(5) (1975), 35–58; Math. USSR-Sb., 26:1 (1975), 31–54

Citation in format AMSBIB
\by N.~B.~Engibaryan, A.~A.~Arutyunyan
\paper Integral equations on the half-line with difference kernels and nonlinear functional equatons
\jour Mat. Sb. (N.S.)
\yr 1975
\vol 97(139)
\issue 1(5)
\pages 35--58
\jour Math. USSR-Sb.
\yr 1975
\vol 26
\issue 1
\pages 31--54

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    This publication is cited in the following articles:
    1. N. B. Engibaryan, L. G. Arabadzhyan, “Systems of Wiener–Hopf integral equations, and nonlinear factorization equations”, Math. USSR-Sb., 52:1 (1985), 181–208  mathnet  crossref  mathscinet  zmath
    2. Arabadzhian L., Engibarian N., “The Factorization of Wiener-Hopf Multidimensional Integral-Operators”, 291, no. 1, 1986, 11–14  mathscinet  isi
    3. Engibaryan N., Arabadzhyan L., “Some Factorization Problems for Convolution Integral-Operators”, Differ. Equ., 26:8 (1990), 1069–1078  mathnet  mathscinet  zmath  isi
    4. N. B. Engibaryan, B. N. Enginbarian, “Convolution equation with a completely monotonic kernel on the half-line”, Sb. Math., 187:10 (1996), 1465–1485  mathnet  crossref  crossref  mathscinet  zmath  isi
    5. N. B. Engibaryan, “Convolution equations containing singular probability distributions”, Izv. Math., 60:2 (1996), 249–280  mathnet  crossref  crossref  mathscinet  zmath
    6. L. G. Arabadzhyan, “On a conservative integral equation with two kernels”, Math. Notes, 62:3 (1997), 271–277  mathnet  crossref  crossref  mathscinet  zmath  isi
    7. B. N. Enginbarian, “Multiple factorization of convolution-type integral operators”, Comput. Math. Math. Phys., 37:4 (1997), 435–446  mathnet  mathscinet  zmath
    8. N. B. Engibaryan, A. Kh. Khachatryan, “Some convolution-type integral equations in kinetic theory”, Comput. Math. Math. Phys., 38:3 (1998), 452–467  mathnet  mathscinet  zmath
    9. N. B. Engibaryan, “Setting and solving several factorization problems for integral operators”, Sb. Math., 191:12 (2000), 1809–1825  mathnet  crossref  crossref  mathscinet  zmath  isi
    10. Norair B. Yengibarian, “Renewal equation on the whole line”, Stochastic Processes and their Applications, 85:2 (2000), 237  crossref  mathscinet  zmath
    11. N. B. Engibaryan, “Conservative systems of integral convolution equations on the half-line and the entire line”, Sb. Math., 193:6 (2002), 847–867  mathnet  crossref  crossref  mathscinet  zmath  isi
    12. Arabadzhyan L., “Factorization of Conservative Integral Convolution Type Operators with Slowly Decaying Kernels”, Differ. Equ., 38:3 (2002), 430–433  mathnet  crossref  mathscinet  zmath  isi
    13. L. G. Arabadzhyan, “The Wiener–Hopf Integral Equation in the Supercritical Case”, Math. Notes, 76:1 (2004), 10–17  mathnet  crossref  crossref  mathscinet  zmath  isi
    14. B. N. Enginbarian, “On the Convolution Equation with Positive Kernel Expressed via an Alternating Measure”, Math. Notes, 81:5 (2007), 620–627  mathnet  crossref  crossref  mathscinet  zmath  isi  elib  elib
    15. L. G. Arabadzhyan, A. S. Khachatryan, “A class of integral equations of convolution type”, Sb. Math., 198:7 (2007), 949–966  mathnet  crossref  crossref  mathscinet  zmath  isi  elib
    16. Khachatryan K.A., “Solvability of vector integro-differential equations of convolution type on the semiaxis”, J. Contemp. Math. Anal., 43:5 (2008), 305–316  crossref  mathscinet  zmath  isi
    17. Khachatryan Kh.A., Khachatryan E.A., “On an Integro-Differential Equation with Almost Difference Kernel on the Half-Line”, Differ. Equ., 44:7 (2008), 935–944  crossref  mathscinet  zmath  isi
    18. Khachatryan Kh.A., “Sufficient conditions for the solvability of the Urysohn integral equation on a half-line”, Dokl. Math., 79:2 (2009), 246–249  mathnet  crossref  mathscinet  zmath  isi  elib
    19. Khachatryan A.Kh., Khachatryan Kh.A., “On Some Systems of Convolution-Type First-Order Integrodifferential Equations on the Semiaxis”, Ukr. Math. J., 61:9 (2009), 1511–1528  crossref  mathscinet  zmath  isi
    20. Kh. A. Khachatryan, H. S. Petrosyan, “One parameter families of positive solutions of some classes of convolution type nonlinear integral equations”, J. Math. Sci., 231:2 (2018), 153–167  mathnet  crossref  crossref
    21. N. B. Engibaryan, “On the factorization of matrix and operator Wiener–Hopf integral equations”, Izv. Math., 82:2 (2018), 273–282  mathnet  crossref  crossref  adsnasa  isi  elib
    22. L. G. Arabadzhyan, “Homogeneous Wiener–Hopf Double Integral Equation with Symmetric Kernel in the Conservative Case”, Math. Notes, 106:1 (2019), 3–10  mathnet  crossref  crossref  isi  elib
    23. Arabajyan L.G., “A Wiener-Hopf Integral Equation With a Nonsymmetric Kernel in the Supercritical Case”, J. Contemp. Math. Anal.-Armen. Aca., 54:5 (2019), 253–262  crossref  isi
  • Математический сборник (новая серия) - 1964–1988 Sbornik: Mathematics (from 1967)
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