Abstract: In
this paper, we study the nonlinear equation of the form
where
is the
Diamond operator iterated k-times,
defined by
is the dimension of the Euclidean
space is an unknown for k is a positive integer and c
is a positive constant.
On
the suitable conditions for f, u
and for the spectrum of the Diamond heat kernel, we can find the unique solution
in the compact subset of Moreover,
if we putandthen we obtain the solution of
nonlinear equation related to the heat equation.
Keywords and phrases: the nonlinear equation, the spectrum, the diamond heat kernel.
