Multi-bump solutions of $-Îu=K(x)u^{\frac{n+2}{n-2}}$ on lattices in $R^n$
arXiv:1305.4698
Abstract
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.
Final version. Some typo corrected. To appear inJournal fur die reine und angewandte Mathematik (Crelle's Journal)