Infinitely many solutions for the Schrödinger equations in RN with critical growth
Infinitely many solutions for the Schrödinger equations in RN with critical growth
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DOI：
10.1016/j.jde.2011.09.032
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发表时间：
2012-02
影响因子：
2.4
通讯作者：
Wenyi Chen;Juncheng Wei;Shusen Yan
中科院分区：
文献类型：
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作者：
Wenyi Chen;Juncheng Wei;Shusen Yan
我们在rn中考虑以下非线性问题，其中V(r)是一个有界的非负函数，N大于或等于5。我们证明了如果r2V(r)有一个局部最大值点，或者有一个局部最小值点r0>，那么（0.1）有无穷多个非径向解，它们的能量可以任意大。作为一个应用，我们表明以下问题的解集具有无界能量，只要λ<−N(N−2)4，N大于或等于5。
We consider the following nonlinear problem in RNwhere V(r) is a bounded non-negative function, N⩾5. We show that if r2V(r) has a local maximum point, or local minimum point r0>0 with V(r0)>0, then (0.1) has infinitely many non-radial solutions, whose energy can be made arbitrarily large. As an application, we show that the solution set of the following problem has unbounded energy, as long as λ<−N(N−2)4, N⩾5.