×

An existence theorem for certain solutions of algebraic differential equations in sectors. (English) Zbl 0307.34005

MSC:

34M99 Ordinary differential equations in the complex domain
34E05 Asymptotic expansions of solutions to ordinary differential equations
34D05 Asymptotic properties of solutions to ordinary differential equations
PDFBibTeX XMLCite
Full Text: Numdam EuDML

References:

[1] S. Bank , On solution having large rate of growth for nonlinear differen, tial equations in the complex domain , J. Math. Anal. Appl. , 22 ( 1968 )-pp. 129 - 143 . MR 252728 | Zbl 0155.12504 · Zbl 0155.12504 · doi:10.1016/0022-247X(68)90165-0
[2] S. Bank , On the instability theory of differential polynomials , Ann. Mat. Pura App L , 74 ( 1966 ), pp. 83 - 111 . MR 204785 | Zbl 0149.29702 · Zbl 0149.29702 · doi:10.1007/BF02416451
[3] S. Bank , On the asymptotic representation of analytic solutions of first order algebraic differential equations in sectors , Trans. Amer. Math. Soc , 176 ( 1973 ) 263 - 283 . MR 320461 | Zbl 0271.34012 · Zbl 0271.34012 · doi:10.2307/1996207
[4] E.W. Chamberlain , Families of principal solutions of ordinary differential equations , Trans. Amer. Math. Soc. , 107 ( 1963 ), pp. 261 - 272 . MR 148974 | Zbl 0121.07201 · Zbl 0121.07201 · doi:10.2307/1993893
[5] W. Strodt , Contributions to the asymptotic theory of ordinary differential equations in the complex domain , Mem. Amer. Math. Soc. , no. 13 ( 1954 ). MR 67290 | Zbl 0059.07701 · Zbl 0059.07701
[6] W. Strodt , On the algebraic closure of certain partially ordered fields , Trans. Amer. Math. Soc. , 105 ( 1962 ), pp. 229 - 250 . MR 140514 | Zbl 0113.03301 · Zbl 0113.03301 · doi:10.2307/1993625
[7] W. Strodt - R. K. WRIGHT, Asymptotic behavior of solutions and adjunction fields for nonlinear first-order differential equations , Mem. Amer. Math. Soc. , no. 109 ( 1971 ). MR 284660 | Zbl 0235.34005 · Zbl 0235.34005
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.