Multi-bump solutions of $-Δu=K(x)u^{\frac{n+2}{n-2}}$ on lattices in $R^n$
Year: 2013
Type: preprint
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.
Source: arXiv (Cornell University)
Authors: Li, YanYan, Wei, Juncheng, Xu, Haoyuan
Language: English
Subfield: Applied Mathematics
Field: Mathematics
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W4394671789