带有扰动项的Hénon方程的多解性研究

Acta mathematica scientia,Series A ›› 2012, Vol. 32 ›› Issue (4): 785-796.

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Multiple Solutions for the Nonlinear Hénon Equation Under Perturbations

ZHU Hong-Bo¹, WANG Zheng-Ping², GUO Yuan-Bin²

1.Faculty of Applied Mathematics, Guangdong University of Technology, Guangzhou 510006； 2.Wuhan Institute of Physics and Mathematics, Chinese Academy of Sciences, Wuhan 430071

Received:2011-11-02 Revised:2012-07-26 Online:2012-08-25 Published:2012-08-25
Supported by:
国家自然科学基金(11026138, 10801132)资助

Abstract

Abstract:

In this paper, we are concerned with the following nonlinear elliptic problem
u(x)=|x|^α|u|^p-2u+h(x), x∈B,
u=0, x∈∂B
Here Ω( R^N, N>4 is smooth and bounded. Applying the perturbation method introduced by Bahari-Berestycki^[3], for any h(x)=h(y, z)=h(|y|, |z|)L²B, x=(y, z)∈
R^l×R^N-l, when α> N+2, we show that there exists p_{N, l}>2 such that for any p∈(2, p_{N, l}), problem (P) has infinity many distinct solutions.

Key words: Hénon equation, Perturbation method, Infinity many distinct solutions

CLC Number:

60F15

ZHU Hong-Bo, WANG Zheng-Ping, GUO Yuan-Bin. Multiple Solutions for the Nonlinear Hénon Equation Under Perturbations[J].Acta mathematica scientia,Series A, 2012, 32(4): 785-796.

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Multiple Solutions for the Nonlinear Hénon Equation Under Perturbations

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