Multi-bump solutions of -Δu=K(x)u^(n+2)/(n-2) on lattices in Rⁿ

2013/05/21 by Yanyan Li, Juncheng Wei, Li, YanYan +3
Mathematics · #Analysis of PDEs (math.AP) #FOS: Mathematics #Nonlinear Differential Equations Analysis

paper · pdf · doi:10.48550/arxiv.1305.4698

openalex publication_date 2013/05/21 · openalex created_date 2024/04/11 · openalex updated_date 2026/07/28

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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