Shijian Tai, Jiangtao Wang
In this article, we study the q-Laplacian equation
where and . We prove that the problem has two solutions when is large, and has two additional solutions when is close to the critical Sobolev exponent . A symmetry-breaking phenomenon appears which shows that the least-energy solution cannot be radial function.
Submitted November 7, 2011. Published January 24, 2012.
Math Subject Classifications: 35J40.
Key Words: Ground state; minimizer; nonradial function; q-Laplacian; Rayleigh quotient.
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| Shijian Tai |
Shenzhen Experimental Education Group
Shenzhen, 5182028, China
| Jiangtao Wang |
School of Statistics and Mathematics
Zhongnan University of Economics and Law
Wuhan, 430073, China
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