We study asymptotic behaviors of positive solutions to a class of Neumann elliptic problems in a bounded domain as the diﬀusion coeﬃcient goes to inﬁnity. At ﬁrst we study a subcritical case and ﬁnd that there is a uniform upper bound for all positive solutions and all of them will approach a constant as the diﬀusion coeﬃcient approches inﬁnity. Secondly, we study a critical case and show the same conclusions hold for least-energy solutions under some assumptions.
- Asymptotic behaviors,
- Neumann elliptic problems