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Infinitely many non-radial solutions for the polyharmonic Hénon equation with a critical exponent

Published online by Cambridge University Press:  16 January 2017

Yuxia Guo
Affiliation:
Department of Mathematics, Tsinghua University, Beijing 100084, People's Republic of China ([email protected])
Bo Li
Affiliation:
Department of Mathematics, Tsinghua University, Beijing 100084, People's Republic of China ([email protected])
Yi Li
Affiliation:
Department of Mathematics and Statistics, Wright State University, Dayton, OH 45435, USA

Extract

We study the following polyharmonic Hénon equation:

where (m)* = 2N/(N – 2m) is the critical exponent, B1(0) is the unit ball in ℝN, N ⩾ 2m + 2 and K(|y|) is a bounded function. We prove the existence of infinitely many non-radial positive solutions, whose energy can be made arbitrarily large.

Type
Research Article
Copyright
Copyright © Royal Society of Edinburgh 2017 

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