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arXiv · 1305.4698

Multi-bump solutions of $-\Delta u=K(x)u^{\frac{n+2}{n-2}}$ on lattices in $R^n$

YanYan Li·Juncheng Wei·Haoyuan Xu
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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.

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YanYan Li, Juncheng Wei, Haoyuan Xu. 2013-05-21. Multi-bump solutions of $-\Delta u=K(x)u^{\frac{n+2}{n-2}}$ on lattices in $R^n$. https://arxiv.org/abs/1305.4698

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