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On some systems of nonlinear integral Hammerstein-type equations on the semiaxis

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Ukrainian Mathematical Journal Aims and scope

We prove the existence for a one-parameter family of solutions of a system of nonlinear integral Hammerstein-type equations on the positive semiaxis and study the asymptotic behavior of the obtained solutions at infinity.

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References

  1. A. Hammerstein, “Nichtlineare Integralgleichungen nebst Anwendungen,” Acta Math., 54, 117–176 (1929).

    Article  MathSciNet  Google Scholar 

  2. P. S. Urysohn, “On one type of nonlinear integral equations,” Mat. Sb., 31, 236–255 (1924).

    Google Scholar 

  3. M. A. Krasnosel’skii, “Criteria of continuity for some nonlinear operators,” Ukr. Mat. Zh., 2, No. 3, 70–86 (1950).

    MathSciNet  Google Scholar 

  4. P. P. Zabreiko, “On the continuity of a nonlinear operator,” Sib. Mat. Zh., 5, No. 4, 958–960 (1964).

    MathSciNet  Google Scholar 

  5. P. P. Zabreiko, “On the continuity and complete continuity of the Urysohn operators,” Dokl. Akad. Nauk SSSR, 161, No. 5, 1007–1010 (1965).

    MathSciNet  Google Scholar 

  6. M. A. Krasnosel’skii, P. P. Zabreiko, E. I. Pustyl’nik, and P. E. Sobolevskii, Integral Operators in the Spaces of Summable Functions [in Russian], Nauka, Moscow (1966).

    Google Scholar 

  7. P. P. Zabreiko and E. I. Pustyl’nik, “On the continuity and complete continuity of nonlinear integral operators in the spaces L p ,” Usp. Mat. Nauk, 19, No. 2, 204–205 (1964).

    Google Scholar 

  8. N. B. Engibaryan and A. Kh. Khachatryan “Problems of the nonlinear theory of dynamics of rarefied gas,” Mat. Model., 16, No. 1, 67–74 (2004).

    MATH  MathSciNet  Google Scholar 

  9. N. B. Engibaryan, “On one problem of nonlinear radiation transport,” Astrofizika, 2, No. 1, 31–36 (1966).

    Google Scholar 

  10. J. D. Sargan, “The distribution of wealth,” Econometrica, 25, 568–590 (1957).

    Article  MATH  MathSciNet  Google Scholar 

  11. V. S. Vladimirov, “On the equation of p-adic open string for a scalar field of tachyons,” Izv. Ros. Akad. Nauk, Ser. Mat., 69, No. 3, 55–80 (2005).

    Google Scholar 

  12. L. G. Arabadzhyan, “Solutions of one integral Hammerstein-type equation,” Izv. Nats. Akad. Nauk Arm., Ser. Mat., 32, No. 1, 21–28 (1997).

    MathSciNet  Google Scholar 

  13. Kh. A. Khachatryan, “Sufficient conditions for the solvability of the Urysohn integral equation on a half line,” Dokl. Mat., 79, No. 2, 246–249 (2009).

    Article  MATH  MathSciNet  Google Scholar 

  14. P. Lankaster, Theory of Matrices, Academic Press, New York (1969).

    Google Scholar 

  15. L. G. Arabadzhyan and N. B. Engibaryan, “Equations in convolutions and nonlinear functional equations,” in: Itogi VINITI. Ser. Mathematical Analysis [in Russian], 22, VINITI, Moscow (1984), pp. 175–242.

  16. N. B. Engibaryan and L. G. Arabadzhyan, “Systems of integral Wiener–Hopf equations and the nonlinear equations of factorization,” Mat. Sb., 124, No. 2, 189–216 (1984).

    MathSciNet  Google Scholar 

  17. A. N. Kolmogorov and S. V. Fomin, Elements of the Theory of Functions and Functional Analysis [in Russian], Nauka, Moscow (1976).

    Google Scholar 

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Translated from Ukrains’kyi Matematychnyi Zhurnal, Vol. 62, No. 4, pp. 552–566, April, 2010.

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Khachatryan, K.A. On some systems of nonlinear integral Hammerstein-type equations on the semiaxis. Ukr Math J 62, 630–647 (2010). https://doi.org/10.1007/s11253-010-0376-9

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  • DOI: https://doi.org/10.1007/s11253-010-0376-9

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