Concentration of solutions for a fourth order elliptic equation in ℝ^N

2011/11/11 by Zhongyuan, Liu
#58\mathrm{E05} #Analysis of PDEs (math.AP) #FOS: Mathematics #Primary 35\mathrm{J}60 #\ Secondary 35\mathrm{J}65

paper · doi:10.48550/arxiv.1111.2712

Abstract

In this paper, we study the following fourth order elliptic problem Δ² u=(1+εK(x)) u^{2^*-1}, x∈ ℝ^N where 2^*=(2N)/(N-4),N≥5, ε>0. We prove that the existence of two peaks solutions for the above problem, if K(x) has two critical points satisfying certain conditions, provided ε is small enough.

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