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
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