Literature Cited
T. Nishimoto, “A turning point problem of an n-th-order differential equation of hydrodynamic type,” Kodai Math. Sem. Repts.,20, 218–256 (1968).
P. E. Tovstik, “Integrals of a linear equation of order m+n with a small parameter for the derivatives,” Diff. Uravn.,6, No. 6, 989–999 (1970).
M. A. Kovalevskii, “The constructions of fundamental families of solutions and the problem of their connections for a linear differential equation of hydrodynamic type with a turning point and a regular singularity,” Diff. Uravn.,18, No. 6, 948–956 (1982).
K. Okubo, “A global representation of a fundamental set of solutions and a Stokes phenomenon for a system of linear ordinary differential equations,” J. Math. Soc. Jpn.,15, No. 3, 268–288 (1963).
H.-G. Roos, “Die Konstruction eines asymptotischen Fundamentalsystems für eine linear Differentialgleichung vom hydrodynamischen Typ,” Z. Angew. Math. Mech.,55, No. 9, 401–407 (1976).
M. Kohno, “A two point connection problem,” Hiroshima Math. J.,9, 61–135 (1979).
M. A. Kovalevskii, “Finding the connections between two fundamental families of solutions of an ordinary linear differential equation,” Vestn. Leningr. Univ., No. 1, 32–37 (1981).
M. A. Kovalevskii, “The construction of a Stokes multiplier for an equation with two singular points,” Vestn. Leningr. Univ., No. 7, 49–54 (1981).
W. Wasow, Asymptotic Expansions for Ordinary Differential Equations, Krieger (1976).
M. A. Kovalevskii, “The uniform asymptotics of an integral connected with a class of entire functions,” Vestn. Leningr. Univ., No. 13, 27–33 (1981).
M. A. Kovalevskii, “The asymptotics of a class of entire functions,” Vestn. Leningr. Univ., No. 19, 19–24 (1981).
M. A. Kovalevskii, “The asymptotic behavior of holomorphic solutions at zero of a linear differential equation,” Vestn. Leningr. Univ., No. 1, 34–39 (1978).
R. A. Handelsman and N. Blaistein, “Asymptotic expansions of integral transforms with oscillatory kernels: a generalization of the method of stationary phase,” SIAM J. Math. Anal.,4, No. 3, 519–535 (1973).
M. A. Evgrafov, Analytic Functions [in Russian], Nauka, Moscow (1965).
M. A. Kovalevskii, “The asymptotics of functions which are generalizations of the Euler gamma-function,” J. Sov. Math.,20, No. 1 (1982).
Additional information
Translated from Sibirskii Matematicheskii Zhurnal, Vol. 25, No. 4, pp. 82–92, July–August, 1984.
Rights and permissions
About this article
Cite this article
Kovalevskii, M.A. Asymptotics of solutions of a standard equation for problems with a turning point. Sib Math J 25, 575–583 (1984). https://doi.org/10.1007/BF00968895
Received:
Issue Date:
DOI: https://doi.org/10.1007/BF00968895