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On a class of Schrödinger systems with critical exponents

Published online by Cambridge University Press:  30 January 2012

Youjun Wang  and
Wenming Zou
Youjun Wang
Affiliation:
Department of Mathematical Sciences, Tsinghua University, Beijing 100084, People's Republic of China (yjwang@math.tsinghua.edu.cn; wzou@math.tsinghua.edu.cn)
Wenming Zou
Affiliation:
Department of Mathematical Sciences, Tsinghua University, Beijing 100084, People's Republic of China (yjwang@math.tsinghua.edu.cn; wzou@math.tsinghua.edu.cn)
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Abstract

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We consider the elliptic system

where N ≥ 4, λ > 0, α1, α2, β ε ℝ, p, p > 1, p + q = 2* = 2N/(N − 2) and α1(x), a2(x) ≥ 0 have potential well. By using variational methods and the category theory, we establish the existence of least energy and multiplicity of solutions.

Type
Research Article
Information
Proceedings of the Royal Society of Edinburgh Section A: Mathematics , Volume 142 , Issue 1 , February 2012 , pp. 199 - 213
Copyright
Copyright © Royal Society of Edinburgh 2012