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- W2011812712 abstract "The paper considers nonlinear partial differential equations of the form $t (partial u/partial t) = F(t,x,u, partial u/partial x)$, with independent variables $(t,x) in mathbb{R} times mathbb{C}$, 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 $F(0,x,0,0)=0$, Re$F_u(0,0,0,0)$ < 0, and $F_v(0,x,0,0)=x^{p+1}gamma(x)$, where $gamma(0) neq 0$ and $p$ is any positive integer. In this case, the equation has a Fuchsian singularity at $t=0$ and an irregular singularity at $x=0$." @default.
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- W2011812712 date "2014-07-01" @default.
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- W2011812712 title "Unique solvability of some nonlinear partial differential equations with Fuchsian and irregular singularities" @default.
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- W2011812712 doi "https://doi.org/10.2969/jmsj/06631017" @default.
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