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Existence of multi-bump solutions for a system with critical exponent in RN
Authors:Jianjun Nie  Yanheng Ding
Institution:1. School of Mathematics and Physics, North China Electric Power University, Beijing 102206, PR China;2. Institute of Mathematics, Academy of Mathematics and Systems Science, Chinese Academy of Sciences, Beijing 100190, PR China
Abstract:We consider the following system with critical exponent in RN:{?Δu=K1(y)u2??1+p2?V(y)up?1vq in RN,?Δv=K2(y)v2??1+q2?V(y)upvq?1 in RN,u,v>0,yRN, where N5, p,q>1 and p+q=2?=2NN?2. Using finite dimensional reduction method, we prove the existence of multi-bump solutions. Their bumps can be placed on arbitrarily many or even infinitely many lattice points in RN. Since p<2 or q<2, we introduce two new norms to avoid singularity.
Keywords:Elliptic system  Critical exponent  Finite dimensional reduction  Multi-bump solutions
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