We treat a nonlinear partial differential equation
F(
x,
u,
ux) = 0 in a neighborhood of
x = 0 ∈
Rd, where
F(
x,
u,
p) is a real-valued smooth function. It is well-known that solutions are constructed by solving noncharacteristic Cauchy problem with the method of characteristics, provided
Fpi(0,0,0) ≠ 0 for some
i. In this paper we study the existence of a classical solution under the condition that
Fpi(0,0,0) = 0 for all 1 ≤
i ≤
d.
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