Electron. J. Diff. Equ.,
Vol. 2013 (2013), No. 109, pp. 116.
Existence of solutions for critical elliptic systems with
boundary singularities
Jianfu Yang, Linli Wu
Abstract:
This article concerns the existence of positive solutions to the
nonlinear elliptic system involving critical HardySobolev exponent
where
and
is a
bounded domain in
,
,
,
,
and
.
Let
be a linear subspace of
such that
, and
be the orthogonal
projection on
with respect to the Euclidean structure.
We consider mainly the case when
and
.
We show that there exists
such that the system above
possesses at least one positive solution for
provided that at each point
the principal curvatures of
at
are nonpositive,
but not all vanish.
Submitted October 16, 2012. Published April 29, 2013.
Math Subject Classifications: 35J25, 25J50, 35J57.
Key Words: Existence; compactness; critical HardySobolev exponent;
nonlinear system.
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Jianfu Yang
Department of Mathematics,
Jiangxi Normal University
Nanchang, Jiangxi 330022, China
email: jfyang_2000@yahoo.com


Linli Wu
Department of Mathematics,
Jiangxi Normal University
Nanchang, Jiangxi 330022, China
email: llwujxsd@sina.com

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