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.
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U2 - 10.2977/prims/1145475358
DO - 10.2977/prims/1145475358
M3 - Article
AN - SCOPUS:24944460190
SN - 0034-5318
VL - 41
SP - 339
EP - 373
JO - Publications of the Research Institute for Mathematical Sciences
JF - Publications of the Research Institute for Mathematical Sciences
IS - 2
ER -