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

Part of: Partial differential equations Elliptic equations and systems

Published online by Cambridge University Press:  16 January 2017

Yuxia Guo ,
Bo Li  and
Yi Li
Yuxia Guo
Affiliation:
Department of Mathematics, Tsinghua University, Beijing 100084, People's Republic of China (yguo@math.tsinghua.edu.cn)
Bo Li
Affiliation:
Department of Mathematics, Tsinghua University, Beijing 100084, People's Republic of China (yguo@math.tsinghua.edu.cn)
Yi Li
Affiliation:
Department of Mathematics and Statistics, Wright State University, Dayton, OH 45435, USA
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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.

Keywords

polyharmonic Hénon equationcritical exponentinfinitely many non-radial solutions

MSC classification

Secondary: 35J65: Nonlinear boundary value problems for linear elliptic equations 35B05: Oscillation, zeros of solutions, mean value theorems, etc. 35B45: A priori estimates
Type
Research Article
Information
Proceedings of the Royal Society of Edinburgh Section A: Mathematics , Volume 147 , Issue 2 , April 2017 , pp. 371 - 396
Copyright
Copyright © Royal Society of Edinburgh 2017