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Uspekhi Mat. Nauk, 1952, Volume 7, Issue 6(52), Pages 3–96 (Mi umn8378)  

This article is cited in 37 scientific papers (total in 39 papers)

Asymptotic laws of distribution of the characteristic values for certain special forms of differential equations of the second order

A. A. Dorodnitsyn


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Citation: A. A. Dorodnitsyn, “Asymptotic laws of distribution of the characteristic values for certain special forms of differential equations of the second order”, Uspekhi Mat. Nauk, 7:6(52) (1952), 3–96

Citation in format AMSBIB
\Bibitem{Dor52}
\by A.~A.~Dorodnitsyn
\paper Asymptotic laws of distribution of the characteristic values for certain special forms of differential equations of the second order
\jour Uspekhi Mat. Nauk
\yr 1952
\vol 7
\issue 6(52)
\pages 3--96
\mathnet{http://mi.mathnet.ru/umn8378}
\mathscinet{http://www.ams.org/mathscinet-getitem?mr=54137}
\zmath{https://zbmath.org/?q=an:0048.32402}


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    This publication is cited in the following articles:
    1. M. A. Evgrafov, M. V. Fedoryuk, “Asymptotic behaviour as $\lambda\to\infty$ of the solution of the equation $w"(z)-p(z,\lambda)w(z)=0$ in the complex $z$-plane”, Russian Math. Surveys, 21:1 (1966), 1–48  mathnet  crossref  mathscinet  zmath
    2. S. A. Lomov, “The construction of asymptotic solutions of certain problems involving parameters”, Math. USSR-Izv., 2:4 (1968), 849–877  mathnet  crossref  mathscinet  zmath
    3. A. Z. Devdariani, “Transitions of electrons from a bound state into the continuous spectrum. Quadratic approximation in a model of a short-range potential”, Theoret. and Math. Phys., 11:2 (1972), 460–469  mathnet  crossref
    4. A. S. Vasilevskii, L. S. Vasilevskii, N. I. Zhirnov, “On an approximate method of solving inverse scattering problems”, Theoret. and Math. Phys., 13:1 (1972), 1015–1023  mathnet  crossref
    5. S. A. Lomov, A. G. Eliseev, “Asymptotic integration of singularly perturbed problems”, Russian Math. Surveys, 43:3 (1988), 1–63  mathnet  crossref  mathscinet  zmath  adsnasa  isi
    6. A. A. Zyablov, “On basis properties of eigenfunctions of one model problem with indefinite weight”, Math. Notes, 54:4 (1993), 1079–1080  mathnet  crossref  mathscinet  zmath  isi
    7. G. A. Aigunov, “On the boundedness problem for the set of orthonormal eigenfunctions for a class of Sturm–Liouville operators with a weight function of unbounded variation on a finite interval”, Math. Notes, 60:3 (1996), 321–323  mathnet  crossref  crossref  mathscinet  zmath  isi  elib
    8. M. K. Kerimov, “On certain special functions that arise in the solution of ordinary differential equations by asymptotic methods”, Comput. Math. Math. Phys., 36:11 (1996), 1547–1566  mathnet  mathscinet  zmath  isi
    9. M. K. Kerimov, “Special functions which occur in the theory of nonlinear oscillations”, Comput. Math. Math. Phys., 36:8 (1996), 1027–1039  mathnet  mathscinet  zmath  isi
    10. V. A. Sadovnichii, V. E. Podolskii, “A class of Sturm–Liouville operators and approximate calculation of the first eigenvalues”, Sb. Math., 189:1 (1998), 129–145  mathnet  crossref  crossref  mathscinet  zmath  isi
    11. V. N. Bobochko, “A boundary value problem for a system of singularly perturbed differential equations with a nondiagonalizable limit operator”, Russian Math. (Iz. VUZ), 43:4 (1999), 12–21  mathnet  mathscinet  zmath  elib
    12. M. K. Kerimov, “On the 90th birthday of academician Anatolii Alekseevich Dorodnitsyn (1910–1994)”, Comput. Math. Math. Phys., 40:12 (2000), 1691–1693  mathnet  mathscinet  zmath
    13. S. N. Tumanov, “Asymptotic formulae for the real eigenvalues of the Sturm–Liouville problem with two turning points”, Izv. Math., 65:5 (2001), 1003–1016  mathnet  crossref  crossref  mathscinet  zmath
    14. Stepin, SA, “Semiclassical spectral asymptotics and the Stokes phenomenon for the Weber equation”, Doklady Mathematics, 63:3 (2001), 306  isi  elib
    15. M. K. Kerimov, “On the 90th birthday of Professor Vitalij Arsen'evich Ditkin (1910–1987)”, Comput. Math. Math. Phys., 41:12 (2001), 1677–1717  mathnet  mathscinet  zmath
    16. V. D. Liseikin, “On the numerical solution of singularly perturbed problems with turning points”, Comput. Math. Math. Phys., 41:1 (2001), 55–83  mathnet  mathscinet  zmath  elib
    17. S. A. Stepin, A. A. Arzhanov, “On localization of the spectrum in a problem in singular perturbation theory”, Russian Math. Surveys, 57:3 (2002), 608–610  mathnet  crossref  crossref  mathscinet  zmath  adsnasa  isi  elib
    18. V. N. Bobochko, “A differential turning point in the theory of singular perturbations. I”, Russian Math. (Iz. VUZ), 46:3 (2002), 1–11  mathnet  mathscinet  zmath  elib
    19. V. N. Bobochko, “A differential turning point in the theory of singular perturbations. II”, Russian Math. (Iz. VUZ), 46:5 (2002), 1–11  mathnet  mathscinet  zmath  elib
    20. N. Ya. Kirpichnikova, V. B. Philippov, S. Yu. Fadeeva, “Combined method calculating the field generated by a point source in a surface wave guide”, J. Math. Sci. (N. Y.), 138:2 (2006), 5543–5548  mathnet  crossref  mathscinet  zmath  elib
    21. Kh. K. Ishkin, “Necessary Conditions for the Localization of the Spectrum of the Sturm–Liouville Problem on a Curve”, Math. Notes, 78:1 (2005), 64–75  mathnet  crossref  crossref  mathscinet  zmath  isi  elib
    22. V. N. Bobochko, “An unstable differential turning point in the theory of singular perturbations”, Russian Math. (Iz. VUZ), 49:4 (2005), 6–14  mathnet  mathscinet  zmath  elib
    23. V. A. Sadovnichii, V. E. Podolskii, “Traces of operators”, Russian Math. Surveys, 61:5 (2006), 885–953  mathnet  crossref  crossref  mathscinet  zmath  adsnasa  isi  elib  elib
    24. N. Ya. Kirpichnikova, S. Yu. Fadeeva, V. B. Philippov, “Diffraction of the near-surface waves on a vertical interface of media”, J. Math. Sci. (N. Y.), 142:6 (2007), 2559–2570  mathnet  crossref  mathscinet  zmath  elib
    25. V. N. Bobochko, “Uniform asymptotics of a solution of an inhomogeneous system of two differential equations with a turning point”, Russian Math. (Iz. VUZ), 50:5 (2006), 6–16  mathnet  mathscinet  zmath  elib
    26. S. I. Kadchenko, I. I. Kinzina, “Computation of eigenvalues of perturbed discrete semibounded operators”, Comput. Math. Math. Phys., 46:7 (2006), 1200–1206  mathnet  crossref  mathscinet  elib
    27. I. I. Kinzina, “Computation of the eigenvalues of a discrete selfadjoint operator perturbed by a bounded operator”, Russian Math. (Iz. VUZ), 52:6 (2008), 13–21  mathnet  crossref  mathscinet  zmath  elib
    28. I. I. Kinzina, “Nakhozhdenie sobstvennykh chisel vozmuschennykh diskretnykh operatorov”, Vestnik ChelGU, 2008, no. 10, 34–43  mathnet
    29. Sadovnichii V.A., Podol'skii V.E., “Traces of differential operators”, Differ. Equ., 45:4 (2009), 477–493  crossref  mathscinet  zmath  isi  elib  elib
    30. M. K. Kerimov, “Special functions in Academician A. A. Dorodnicyn's scientific legacy: Special functions associated with the van der Pol equation”, Comput. Math. Math. Phys., 51:5 (2011), 781–802  mathnet  crossref  mathscinet  isi
    31. M. K. Kerimov, “Special functions in academician A. A. Dorodnicyns scientific legacy: Special functions arising in the solution of boundary value problems for second-order singular ordinary differential equations by asymptotic methods”, Comput. Math. Math. Phys., 51:11 (2011), 1878–1914  mathnet  crossref  mathscinet  isi
    32. M. K. Kerimov, “The theory of regularized traces of Sturm–Liouville operators as applied to approximate calculation of eigenvalues and eigenfunctions of certain singular operators”, Comput. Math. Math. Phys., 51:12 (2011), 2079–2101  mathnet  crossref  mathscinet  isi
    33. Maleko E.M., “O metode sledov rezolvent, vychislennykh tochno”, Vestnik Samarskogo gosudarstvennogo universiteta, 2011, no. 86, 37–52  mathnet  elib
    34. M. K. Kerimov, “Approximate computation of eigenvalues and eigenfunctions of Sturm–Liouville differential operators by applying the theory of regularized traces”, Comput. Math. Math. Phys., 52:3 (2012), 351–386  mathnet  crossref  zmath  adsnasa  isi  elib  elib
    35. M. K. Kerimov, “The theory of regularized traces of operators as applied to approximate computation of eigenvalues and eigenfunctions of fluid dynamics problems”, Comput. Math. Math. Phys., 52:5 (2012), 756–786  mathnet  crossref  mathscinet  isi  elib  elib
    36. I. A. Zelenskaya, “A system of singularly perturbed equations with differential turning point of the 1st kind”, Russian Math. (Iz. VUZ), 59:3 (2015), 55–65  mathnet  crossref
    37. Kh. K. Ishkin, “Localization criterion for the spectrum of the Sturm–Liouville operator on a curve”, St. Petersburg Math. J., 28:1 (2017), 37–63  mathnet  crossref  mathscinet  isi  elib
    38. S. A. Kaschenko, “Asimptoticheskie zakony raspredelenii sobstvennykh znachenii periodicheskoi i antiperiodicheskoi kraevykh zadach dlya differentsialnykh uravnenii vtorogo poryadka”, Model. i analiz inform. sistem, 24:1 (2017), 13–30  mathnet  crossref  mathscinet  elib
    39. S. A. Stepin, V. V. Fufaev, “The phase-integral method in a problem of singular perturbation theory”, Izv. Math., 81:2 (2017), 359–390  mathnet  crossref  crossref  mathscinet  adsnasa  isi  elib
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