Yibin Zhang, Haitao Yang
Let be a bounded domain in with smooth boundary and , we study the Neumann problem for the Henon equation
where denotes the outer unit normal vector to , and p is a large exponent. In a constructive way, we show that, as p approaches , such a problem has a family of positive solutions with arbitrarily many interior and boundary spikes involving the origin. The same techniques lead also to a more general result on Henon-type weights.
Submitted October 14, 2014. Published March 26, 2015.
Math Subject Classifications: 35J25, 35J20, 58K05.
Key Words: Mixed interior and boundary peak solutions; Henon-type weight; large exponent; Lyapunov-Schmidt reduction process.
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| Yibin Zhang |
College of Sciences, Nanjing Agricultural University
Nanjing 210095, China
| Haitao Yang |
Department of Mathematics, Zhejiang University
Hangzhou 310027, China
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