Existence of positive solutions of the equation −Δu + a(x)u = u(N + 2)(N − 2) in RN
Existence of positive solutions of the equation −Δu + a(x)u = u(N + 2)(N − 2) in RN
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DOI：
10.1016/0022-1236(90)90120-a
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发表时间：
1990
影响因子：
1.7
通讯作者：
V. Benci;G. Cerami
中科院分区：
文献类型：
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作者：
V. Benci;G. Cerami
[N (N-2)] ' N-2 " 4 (1+~ X~ 2) VW~，所有正解都可以通过平移和尺度变化得到（参见Cl]，[ll],[18]）。然而，如果q# RN或a (x) $0，情况就不那么简单了。例如，如果q# RN和a (x)= 1，常数，作为著名的Pohozaev恒等式[15]的结果，可以得出，如果Q是一个有界星形区域[xv> 0 on &Z！]，当A3为0时，（1.1）无解，而当Sz为补为星形[x]的无界域时。当I< 0时，在dQ上v< 0]（1.1）无解。此外，如果Q= R ‘ ’且a (x)= l# 0，则Pohozaev恒等式[5]的广义版constant给出cl u* dx= 0
[N (N-2)]‘N-2” 4 (1+~ X~ 2) VW~ and all the positive solutions can be obtained by this one by translations and scale changes (cf. Cl],[ll],[18]). However, if Q# RN or a (x) $0 the situation is not so simple. For example if Q# RN and a (x)= 1, constant, as a consequence of the famous Pohozaev identity [15], it follows that implies if Q is a bounded starshaped domain [xv> 0 on &Z!] that (1.1) has no solutions if A3 0, while if Sz is an unbounded domain whose complement is starshaped [x. v< 0 on dQ](1.1) has no solutions if I< 0. Moreover if Q= R” and a (x)= L# 0, constant, a generalized version of the Pohozaev identity [5], gives cl u* dx= O