Daisuke Naimen
Abstract:
We consider the nonlinear Neumann boundary-value problem
where
and
is a bounded domain
with smooth boundary. We suppose a and b are possibly sign-changing
functions in
and on
respectively.
Under some additional assumptions on a and b, we show that there
are infinitely many solutions for sufficiently small
if
. When
, we use the concentration compactness
argument to ensure the PS condition for the associated functional.
We also consider a general problem including the supercritical case and
obtain the existence of infinitely many solutions.
Submitted May 30, 2014. Published August 27, 2014.
Math Subject Classifications: 35J20, 35J60, 35J65.
Key Words: Nonlinear Neumann; elliptic; variational method; critical point.
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Daisuke Naimen Faculty of Science, Graduate School of Science Osaka City University 3-3-138 Sugimoto Sumiyoshi-ku, Osaka-shi Osaka 558-8585, Japan email: d12sax0J51@ex.media.osaka-cu.ac.jp |
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