摘要
This paper concerns the following nonlinear elliptic equation:{?u + K(y)u^((N+2)/(N-2)±ε)= 0, u > 0, y ∈ R^N,u ∈ D^(1,2)(R^N),where ε > 0, N≥5, K(y) is positive and radially symmetric. We show that, under some local conditions on K(y), this problem has large number of bubble solutions if ε is small enough. Moreover, for each m ∈ [2, N- 2),there exists solutions whose functional energy is in the order of ε^(-(N-2-m)/((N-2)~2)).
This paper concerns the following nonlinear elliptic equation：{？u ＋ K（y）u^（（N＋2）/（N-2）±ε）= 0, u 〉 0, y ∈ R^N,u ∈ D^（1,2）（R^N）,where ε 〉 0, N≥5, K（y） is positive and radially symmetric. We show that, under some local conditions on K（y）, this problem has large number of bubble solutions if ε is small enough. Moreover, for each m ∈ [2, N- 2）,there exists solutions whose functional energy is in the order of ε^（-（N-2-m）/（（N-2）~2））.
基金
Tian Yuan Special Funds of National Natural Science Foundation of China (Grant No. 11426088)
