Die Konstruktion asymptotischer Fundamentalsysteme für lineare Differentialgleichungen mit Wendepunkten

Roos, Hans-Georg

Commentationes Mathematicae Universitatis Carolinae, Tome 20 (1979) no. 2, pp. 195-205

Détail

Classification : 34E20

Bibliographie

[1] ANYANWU D. U.: Uniform asymptotic solution of nonhomogeneous differential equations with turning points. SIAM J. Math. Anal. 8 (1977), 710-718. | MR

[2] ANYANWU D. U., KELLER J. B.: A solution of higher order differential equations with several turning points. Comm. pure appl. Math. 31 (1978), 107-121. | MR

[3] BAKKEN I.: On the central connection problem for a class of ordinary differential equations. Funkcial. Ekvac. 20 (1977), 115-156. | MR

[4] BRAAKSMA B. L. J.: Recessive solutions of linear differential equations with polynomial coefficients. Lecture Notes Math. 280 (1972), 1-15. | MR | Zbl

[5] EВГРАФОВ M. A., ФЕДОРЮК M. B.: Accимптотикаa peшений $W^\ast - p(x,\lambda)w = 0$ npи $X\rightarrow\infty$ в комплексной плоскости $z$. Успехи матем. наук 21 (1966), 3-50.

[6] GROEN P. P. N.: Singular perturbed differential operators of second order. Amsterdam 1976.

[7] IWANO M., SIBUYA A.: Reduction of the order of linear ordinary differential equation containing a small parameter. Kodai math. sem. rep. 15 (1963), 1-23. | MR

[8] JURKAT W. B.: Meromorphe Differentialgleichungen. Lecture Notes Math. 637 (1978). | MR | Zbl

[9] LEE R.: On the uniform simplification of linear differential equations in a full neighborhood of a turning point. J. Math. Anal. Appl. 27 (1969), 601-510. | MR

[10] LEUNG A.: Connection formulas for asymptotic solutions of second order turning points in unbounded domains. SIAM J. Math. Anal. 4 (1973), 89-103 (Errata: 6 (1975), 600). | MR | Zbl

[11] LEUNG A.: Lateral connections for asymptotic solutions around higher order turning points. J. Math. Anal. Appl. 50 (1975), 560-578. | MR | Zbl

[12] LEUNG A.: Doubly asymptotic series for $n$-th order differential equations. SIAM J. Math. Anal. 5 (1974), 187-201. | MR | Zbl

[13] LEUNG A.: A dubly asymptotic existence theorem and application to order reduction. Proc. London Math. Soc. 33 (1976), 151-176. | MR

[14] LEUNG A.: A third-order linear differential equation on the real line with two turning points. J. diff. equ. 29 (1978), 304-328. | MR | Zbl

[15] LYNN R., KELLER J.: Uniform asymptotic solutions of second order linear ordinary differential equations with turning points. Comm. Pure Appl. Math, 23 (1970), 379-408. | MR | Zbl

[16] MC HUGH J.: A historical survey of ordinary linear differential equations with a large parameter and turning points. Arch. History Exact. Sci. 7 (1971), 277-324. | MR

[17] NAKAKO M., NISHIMOTO T.: On a secondary turning point problem. Kodai Math. Sem. Rep. 22 (1970), 365-384. | MR

[18] NISHIMOTO T.: On matching methods in turning point problems. Kodai Math. Sem. Rep. 17 (1965), 198-221. | MR | Zbl

[19] NISHIMOTO T.: On a matching method for a linear ordinary differential equation containing a small parameter. Kodai Math. Sem. Rep. 17 (1965), 307-328, 18 (1966), 61-86, 19 (1967), 80-94.

[20] NISHIMOTO T.: On the central connection problem at a turning point. Kodai Math. Sem. Rep. 22 (1970), 30-44. | MR | Zbl

[21] NISHIMOTO T.: On an extension theorem and its application for turning point problems of large order. Kodai Math. Sem. Rep. 25 (1973), 458-489. | MR | Zbl

[22] NISHIMOTO T.: Asymptotic behaviour of the WKB approximations near a Stokes curve. Kodai Math. Sem. Rep. 29 (1977), 71-87. | MR

[23] OLVER F.: Asymptotic and special functions. Academic press, New York 1974.

[24] OLVER F.: Connection formulas for second order differential equations with multiple turning points. SIAM J. Math. Anal. 8 (1977), 127-154. | MR | Zbl

[25] OLVER F.: Connection formulas for second order differential equations having an arbitrary number of turning points of arbitrary multiplicites. SIAM J. Math. Anal. 8 (1977), 673-700. | MR

[26] OLVER F.: Sufficient conditions for Ackerberg-O'Malley resonance. SIAM J. Math. Anal. 9 (1978), 328-355. | MR | Zbl

[27] ROOS H.-G.: Die asymptotische Lösung einer linearen Differentialgleichung zweiter Qrdnung mit zweisegmentigen charakteristischen Polygon. Beiträge zur Analysis 7 (1975), 55-63. | MR

[28] ROOS H.-G.: Die Konstruktion eines asymptotischen Fundamentalsystems für eine lineare Differentialgleichung vom hydrodynamischen Typ. ZAMM 56 (1976), 401-408. | MR | Zbl

[29] ROOS H.-G.: Die asymptotische Lösung einer linearen Differentialgleichung mit dreisegmentigem charaktetistischen Polygon. Mathematische Nachrichten (im Druck).

[30] RUBENFELD L., WILLNER B.: Uniform asymptotic solution for linear second order ordinary differential equations with turning points. SIAM J. Appl. Math. 32 (1977), 21-38. | MR

[31] SIBUYA Y.: Uniform simplification in a full neighborhood of a transition point. Mem. Amer. Math. Soc. no 149 (1974). | MR | Zbl

[32] SIBUYA Y.: Global theory of second order linear ordinary differential equations with a polynomial coefficient. North Holland Math. Studies 18, Amsterdam 1975.

[33] WASOW W.: Asymptotic expansions fee ordinary differential equations. Interscience, New York 1965.

[34] WASOW W.: The central connection problem at turning points of linear differential equations. Comment. Math. Helv. 46 (1971), 65-86. | MR | Zbl

[35] WASOW W.: Simple turning-point problems in unbounded domains. SIAM J. Math. Anal. 1 (1970), 153-170. | MR | Zbl

[36] WILLNER B., RUBENFELD L.: Uniform asymptotic solution for a linear ordinary differential equation with one $\mu $-th order turning point. Comm. Pure Appl. Math. 29 (1976), 343-367. | MR

[37] WYRWIGH H.: An explicit solution of the central connection problem for an $n$-th order linear ordinary differential equation with polynomial coefficients. SIAM J. Math. Anal. 8 (1977), 412-422. | MR