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Proceedings of the American Mathematical Society

Published by the American Mathematical Society since 1950, Proceedings of the American Mathematical Society is devoted to shorter research articles in all areas of pure and applied mathematics.

ISSN 1088-6826 (online) ISSN 0002-9939 (print)

The 2020 MCQ for Proceedings of the American Mathematical Society is 0.85.

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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


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
  • Email:
  • 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:
  • MathSciNet review: 2869119