Non-even least energy solutions of the Emden-Fowler equation

Author:
Ryuji Kajikiya

Journal:
Proc. Amer. Math. Soc. **140** (2012), 1353-1362

MSC (2010):
Primary 34B15, 34B18

DOI:
https://doi.org/10.1090/S0002-9939-2011-11172-9

Published electronically:
August 4, 2011

MathSciNet review:
2869119

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Abstract | References | Similar Articles | Additional Information

Abstract: In this paper, we study the Emden-Fowler equation whose coefficient is even in the interval under the Dirichlet boundary condition. We prove that if the density of the coefficient function is thin in the interior of and thick on the boundary, then a least energy solution is not even. Therefore the equation has at least three positive solutions: the first one is even, the second one is a non-even least energy solution and the third one is the reflection .

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Additional Information

**Ryuji Kajikiya**

Affiliation:
Department of Mathematics, Faculty of Science and Engineering, Saga University, Saga, 840-8502, Japan

Email:
kajikiya@ms.saga-u.ac.jp

DOI:
https://doi.org/10.1090/S0002-9939-2011-11172-9

Keywords:
Emden-Fowler equation,
least energy solution,
non-even positive solution,
variational method

Received by editor(s):
January 4, 2011

Published electronically:
August 4, 2011

Additional Notes:
The author was supported in part by Grant-in-Aid for Scientific Research (C) (No. 20540197), Japan Society for the Promotion of Science

Communicated by:
Yingfei Yi

Article copyright:
© Copyright 2011
American Mathematical Society

The copyright for this article reverts to public domain 28 years after publication.