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Non-even positive solutions of the Emden–Fowler equations with sign-changing weights

Published online by Cambridge University Press:  22 May 2013

Ryuji Kajikiya
Ryuji Kajikiya*
Affiliation:
Department of Mathematics, Faculty of Science and Engineering, Saga University, Saga 840-8502, Japan (kajikiya@ms.saga-u.ac.jp)
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Abstract

We study the Emden–Fowler equation whose coefficient function is even in the interval (—1, 1), negative near t = 0 and positive near t = ±1. Then we prove that a least energy solution is not even. Therefore, the equation has an even positive solution and a non-even positive solution.

Type
Research Article
Information
Proceedings of the Royal Society of Edinburgh Section A: Mathematics , Volume 143 , Issue 3 , June 2013 , pp. 631 - 642
Copyright
Copyright © Royal Society of Edinburgh 2013 

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