@article{Grigorev:1991aa,
    Abstract = {{$[$}We generalize the Newton polygon procedure for algebraic equations to generate solutions of polynomial differential equations of the form ∑∞i=0 {$\alpha$}ix {$\beta$}i where the {$\alpha$}i are complex numbers and the {$\beta$}i are real numbers with {\$}{$\backslash$}beta{\\_}0 > {$\backslash$}beta{\\_}1 > {$\backslash$}cdots{\$}. Using the differential version of the Newton polygon process, we show that any such a series solution is finitely determined and show how one can enumerate all such solutions of a given polynomial differential equation. We also show that the question of deciding if a system of polynomial differential equations has such a power series solution is undecidable.{$]$}},
    Author = {Grigor'ev, D. Yu. and Singer, M. F.},
    BookTitle = {Transactions of the American Mathematical Society},
    File = {Solving Ordinary Differential Equations in Terms of Series with Real Exponents - real\_exponents - a - f.pdf},
    ISBN = {00029947},
    Month = {2020/10/24/},
    Number = {1},
    Pages = {329--351},
    Publisher = {American Mathematical Society},
    Title = {Solving Ordinary Differential Equations in Terms of Series with Real Exponents},
    URL = {http://www.jstor.org/stable/2001845},
    Volume = {327},
    Year = {1991},
    bdsk-url-1 = {http://www.jstor.org/stable/2001845},
    bdsk-url-2 = {https://doi.org/10.2307/2001845},
    c1 = {Full publication date: Sep., 1991},
    date-added = {2020-10-24 13:24:38 +0200},
    date-modified = {2020-10-24 13:24:38 +0200},
    db = {JSTOR},
    ty = {JOUR},
    doi = {10.2307/2001845}
}

@article{Grigorev:1991aa, Abstract = {{$[$}We generalize the Newton polygon procedure for algebraic equations to generate solutions of polynomial differential equations of the form ∑∞i=0 {$\alpha$}ix {$\beta$}i where the {$\alpha$}i are complex numbers and the {$\beta$}i are real numbers with {\$}{$\backslash$}beta{\}0 > {$\backslash$}beta{\}1 > {$\backslash$}cdots{\$}. Using the differential version of the Newton polygon process, we show that any such a series solution is finitely determined and show how one can enumerate all such solutions of a given polynomial differential equation. We also show that the question of deciding if a system of polynomial differential equations has such a power series solution is undecidable.{$]$}}, Author = {Grigor'ev, D. Yu. and Singer, M. F.}, BookTitle = {Transactions of the American Mathematical Society}, File = {Solving Ordinary Differential Equations in Terms of Series with Real Exponents - real_exponents - a - f.pdf}, ISBN = {00029947}, Month = {2020/10/24/}, Number = {1}, Pages = {329--351}, Publisher = {American Mathematical Society}, Title = {Solving Ordinary Differential Equations in Terms of Series with Real Exponents}, URL = {http://www.jstor.org/stable/2001845}, Volume = {327}, Year = {1991}, bdsk-url-1 = {http://www.jstor.org/stable/2001845}, bdsk-url-2 = {https://doi.org/10.2307/2001845}, c1 = {Full publication date: Sep., 1991}, date-added = {2020-10-24 13:24:38 +0200}, date-modified = {2020-10-24 13:24:38 +0200}, db = {JSTOR}, ty = {JOUR}, doi = {10.2307/2001845} }