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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
Published electronically: August 4, 2011
MathSciNet review: 2869119
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Abstract: In this paper, we study the Emden-Fowler equation whose coefficient is even in the interval $(-1,1)$ under the Dirichlet boundary condition. We prove that if the density of the coefficient function is thin in the interior of $(-1,1)$ 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 $u(t)$ and the third one is the reflection $u(-t)$.

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Additional Information

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

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.