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Abstract
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We construct positive solutions to the equation
on the Heisenberg group, singular in the origin, similar
to the Fowler solutions of the Yamabe equations on
. These satisfy the
homogeneity property
for some
large
enough, where
and
is the natural
dilation in
.
We use the Lyapunov–Schmidt method applied to a family of approximate solutions
built by periodization from the global regular solution classified by Jerison and Lee
(1988).
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Keywords
subelliptic equations, perturbation methods
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Mathematical Subject Classification 2010
Primary: 35H20, 35J20, 35J61, 35R03
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Milestones
Received: 6 August 2019
Accepted: 11 October 2019
Published: 29 April 2020
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