### Abstract

Quchi ([2], [3]) found a formal solution (t, x) = Sum_{kG0} uk(x)t^{k} with Equation presented for some class of nonlinear partial differential equations. For these equations he showed that there exists a genuine solution u S(t,x) on a sector S with asymptotic expansion u S(t, x) -(t, x) as t → 0 in the sector S. These equations have polynomial type nonlinear terms. In this paper we study a similar class of equations with the following nonlinear terms Equation presented It is main purpose to get a solvability of the equation in a category u S(t, x) -0 as t → 0 in a sector S. We give a proof by the method that is a little different from that in [3], Further we give a remark that the similar class of equations has a genuine solution u S(t, x) with u S(t, x) -(t, x) as t → 0 in the sector S.

Original language | English |
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Pages (from-to) | 131-145 |

Number of pages | 15 |

Journal | Tokyo Journal of Mathematics |

Volume | 36 |

Issue number | 1 |

DOIs | |

Publication status | Published - 2013 Jun 1 |

### Keywords

- Formal solutions
- Genuine solutions
- Gevrey class

### ASJC Scopus subject areas

- Mathematics(all)