$R^n$中$-Δu=K(x)u^{\frac{n+2}{n-2}}$在格点上的多凸点解
Multi-bump solutions of $-Δu=K(x)u^{\frac{n+2}{n-2}}$ on lattices in $R^n$
摘要：
考虑临界指数半线性椭圆型方程，系数K（x）的前k个变量为周期，其中2k小于n-2.在K上的某些自然条件下，在临界点附近，我们证明了多凸点解的存在性，其中凸点的中心可以放在Rk中的某些格点上，包括无限格点.我们还表明，对于2k大于或等于n-2，没有这样的解决方案存在。
英文摘要：
We consider critical exponent semi-linear elliptic equation with coefficient K(x) periodic in its first k variables, with 2k smaller than n-2. Under some natural conditions on K near a critical point, we prove the existence of multi-bump solutions where the centers of bumps can be placed in some lattices in Rk, including infinite lattices. We also show that for 2k greater than or equal to n-2, no such solutions exist.
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