On the asymptotic representation of analytic solutions of first-order algebraic differential equations in sectors

Author:
Steven Bank

Journal:
Trans. Amer. Math. Soc. **176** (1973), 263-283

MSC:
Primary 34E05; Secondary 34A20

MathSciNet review:
0320461

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Abstract: In this paper, we treat first-order algebraic differential equations whose coefficients belong to a certain type of function field. (Our results include as a special case, the case when the coefficients are rational functions.) In our main result, we obtain precise asymptotic representations for a broad class of solutions of such equations.

**[1]**Steven Bank,*A representation theorem for large and small analytic solutions of algebraic differential equations in sectors*, Trans. Amer. Math. Soc.**159**(1971), 293–305. MR**0283272**, 10.1090/S0002-9947-1971-0283272-2**[2]**Steven Bank,*On solutions having large rate of growth for nonlinear differential equations in the complex domain*, J. Math. Anal. Appl.**22**(1968), 129–143. MR**0252728****[3]**Steven Bank,*On the instability theory of differential polynomials*, Ann. Mat. Pura Appl. (4)**74**(1966), 83–111. MR**0204785****[4]**Erling William Chamberlain,*Families of principal solutions of ordinary differential equations.*, Trans. Amer. Math. Soc.**107**(1963), 261–272. MR**0148974**, 10.1090/S0002-9947-1963-0148974-2**[5]**E. W. Chamberlain,*The univalence of functions asymptotic to nonconstant logarithmic monomials*, Proc. Amer. Math. Soc.**17**(1966), 302–309. MR**0190311**, 10.1090/S0002-9939-1966-0190311-X**[6]**Walter Strodt,*Contributions to the asymptotic theory of ordinary differential equations in the complex domain*, Mem. Amer. Math. Soc.,**No. 13**(1954), 81. MR**0067290****[7]**Walter Strodt,*Principal solutions of ordinary differential equations in the complex domain*, Mem. Amer. Math. Soc.**No. 26**(1957), 107. MR**0092901****[8]**Walter Strodt,*On the algebraic closure of certain partially ordered fields*, Trans. Amer. Math. Soc.**105**(1962), 229–250. MR**0140514**, 10.1090/S0002-9947-1962-0140514-6**[9]**Walter Strodt and Robert K. Wright,*Asymptotic behavior of solutions and adjunction fields for nonlinear first order differential equations*, Memoirs of the American Mathematical Society, No. 109, American Mathematical Society, Providence, R.I., 1971. MR**0284660**

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Additional Information

DOI:
http://dx.doi.org/10.1090/S0002-9947-1973-0320461-4

Keywords:
Algebraic differential equations,
analytic solutions,
representation of solutions,
asymptotic behavior of solutions

Article copyright:
© Copyright 1973
American Mathematical Society