欧米茄
有界函数
领域(数学分析)
组合数学
物理
类型(生物学)
指数
退化(生物学)
数学物理
数学
数学分析
量子力学
生物
哲学
生物信息学
语言学
生态学
作者
Imene Bendahou,Zied Khemiri,Fethi Mahmoudi
出处
期刊:Discrete and Continuous Dynamical Systems
[American Institute of Mathematical Sciences]
日期:2020-01-01
卷期号:40 (4): 2367-2391
被引量:2
摘要
Given a smooth bounded domain $ \Omega \subset \mathbb {R}^n $ and consider the problem \begin{document}$ \left\{\begin{array} {cccccc} - \Delta u = |u|^p - \sigma &\hbox{in } \Omega \\ \dfrac{\partial u}{\partial \nu} = 0 &\hbox{on}\ \partial \Omega \end{array}\right. $\end{document} where $ p $ is subcritical exponent ($ p > 1 $ if $ n = 2 $ and $ 1 < p < \frac{n+2}{n-2} $ if $ n \geq 3 $), $ \sigma > 0 $ is a large parameter and $ \nu $ denotes the outward normal of $ \partial\Omega $. Let $ \Gamma $ be an interior straighline intersecting orthogonally with $ \partial\Omega $. Assuming moreover that $ \Gamma $ satisfies a non-degeneracy condition, we construct a new class of solutions which consist of large number of spikes concentrating on $ \Gamma $, showing as in [5,6] that higher dimensional concentration can exist without resonance condition.
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