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

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- by Ryuji Kajikiya PDF
- Proc. Amer. Math. Soc.
**140**(2012), 1353-1362 Request permission

## 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 $u(-t)$.## References

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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
- 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
- © Copyright 2011
American Mathematical Society

The copyright for this article reverts to public domain 28 years after publication. - 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
- MathSciNet review: 2869119