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

Kajikiya, Ryuji

doi:10.1090/S0002-9939-2011-11172-9

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 $u(-t)$.

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