Infinitely many peak solutions for a biharmonic equation involving critical exponent

Abstract

In this paper, we study the following biharmonic equation normalΔ2u=K(|y|)up,3.0235ptu>0,in3.0235ptB1(0),u=normalΔu=0,0.3em0.3em0.3em0.3emon3.0235pt∂B1(0), where p=N+4N−4, K(1) > 0,K′(1) > 0, B1(0) is the unit ball in double-struckRN(N≥6). We show that the aforementioned problem has infinitely many peak solutions, whose energy can be made arbitrarily large. Copyright © 2016 John Wiley & Sons, Ltd.