On the perturbed Q-curvature problem on S4

JOURNAL OF DIFFERENTIAL EQUATIONS

卷:255

Article

Prashanth, S.¹  Santra, Sanjiban²  Sarkar, Abhishek¹ 

[1] TIFR CAM, Bangalore 560055, Karnataka, India

[2] Univ Sydney, Sch Math & Stat, Sydney, NSW 2006, Australia

关键词: Perturbed problem;    Exponential nonlinearity;    Uniqueness;    Multiplicity;   

DOI  :  10.1016/j.jde.2013.06.015

来源: Elsevier

【 摘 要 】

Let go denote the standard metric on S-4 and P-g0 = Delta(2)(g0) - 2 Delta(g0) denote the corresponding Paneitz operator. In this work, we study the following fourth order elliptic problem with exponential nonlinearity P(g0)u + 6 = 2 Q (x)e(4u) on S-4. Here Q is a prescribed smooth function on S-4 which is assumed to be a perturbation of a constant. We prove existence results to the above problem under assumptions only on the shape of Q near its critical points. These are more general than the non-degeneracy conditions assumed so far. We also show local uniqueness and exact multiplicity results for this problem. The main tool used is the Lyapunov-Schmidt reduction. Crown Copyright (C) 2013 Published by Elsevier Inc. All rights reserved.

【 授权许可】

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