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摘要
The paper considers nonlinear partial differential equations of the form t(partial derivative u/partial derivative t) = F(t, x, u, partial derivative u/partial derivative x), with independent variables (t, x) is an element of R x C, and where F(t, x, u, v) is a function continuous in t and holomorphic in the other variables. It is shown that the equation has a unique solution in a sectorial domain centered at the origin under the condition that F(0, x, 0, 0) = 0, ReFu (0, 0, 0, 0) < 0, and F-v (0, x, 0, 0) = x(p+1)gamma(x), where gamma(0) not equal 0 and p is any positive integer. In this case, the equation has a Fuchsian singularity at t = 0 and an irregular singularity at x = 0.
- 出版日期2014-7
