Solving ordinary differential equations in terms of series with real exponents

摘要: We generalize the Newton polygon procedure for algebraic equations to generate solutions of polynomial differential form EI=O ckix4 where cki are complex numbers and ,Bi real with tio > 31 *fi. Using version process, we show that any such a series solution is finitely determined how one can enumerate all given equation. also question deciding if system has power undecidable. When looks equations, forced deal question: what these have? The first natural class set formal series. An algorithm determine whether coefficients in C(x) [DL84]. Even only consider not enough; must fractional (Puiseux series). In this paper Ea=0 cBiX4' cta E C ,Si Di wBo ,81 * . §1, (Theorem 1.1) satisfies equation, then have no finite limit point. particular Ea.=Oxl/i This motivates us introduce