### Abstract

Let us consider the following nonlinear singular partial differential equation (t∂/∂t)^{m} u = F(t, x, {(t∂/∂t) ^{j} (∂/∂x)^{α} u} _{j+|α|≤m,j<m}) in the complex domain. When the equation is of Fuchsian type with respect to t, holomorphic and singular solutions were investigated quite well by Gérard-Tahara under some assumptions on characteristic exponents. In this paper, the same type of equations is solved in the general case without any assumption on characteristic exponents.

Original language | English |
---|---|

Pages (from-to) | 339-373 |

Number of pages | 35 |

Journal | Publications of the Research Institute for Mathematical Sciences |

Volume | 41 |

Issue number | 2 |

Publication status | Published - 2005 Jul |

Externally published | Yes |

### ASJC Scopus subject areas

- Mathematics(all)

### Cite this

**Structure of solutions of nonlinear partial differential equations of Gérard-Tahara type.** / Tahara, Hidetoshi; Yamazawa, Hiroshi.

Research output: Contribution to journal › Article

*Publications of the Research Institute for Mathematical Sciences*, vol. 41, no. 2, pp. 339-373.

}

TY - JOUR

T1 - Structure of solutions of nonlinear partial differential equations of Gérard-Tahara type

AU - Tahara, Hidetoshi

AU - Yamazawa, Hiroshi

PY - 2005/7

Y1 - 2005/7

N2 - Let us consider the following nonlinear singular partial differential equation (t∂/∂t)m u = F(t, x, {(t∂/∂t) j (∂/∂x)α u} j+|α|≤m,j) in the complex domain. When the equation is of Fuchsian type with respect to t, holomorphic and singular solutions were investigated quite well by Gérard-Tahara under some assumptions on characteristic exponents. In this paper, the same type of equations is solved in the general case without any assumption on characteristic exponents.

AB - Let us consider the following nonlinear singular partial differential equation (t∂/∂t)m u = F(t, x, {(t∂/∂t) j (∂/∂x)α u} j+|α|≤m,j) in the complex domain. When the equation is of Fuchsian type with respect to t, holomorphic and singular solutions were investigated quite well by Gérard-Tahara under some assumptions on characteristic exponents. In this paper, the same type of equations is solved in the general case without any assumption on characteristic exponents.

UR - http://www.scopus.com/inward/record.url?scp=24944460190&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=24944460190&partnerID=8YFLogxK

M3 - Article

AN - SCOPUS:24944460190

VL - 41

SP - 339

EP - 373

JO - Publications of the Research Institute for Mathematical Sciences

JF - Publications of the Research Institute for Mathematical Sciences

SN - 0034-5318

IS - 2

ER -