The asymptotically linear Hénon problem
Keyword(s):
In this paper, we consider the Hénon problem in the ball with Dirichlet boundary conditions. We study the asymptotic profile of radial solutions and then deduce the exact computation of their Morse index when the exponent [Formula: see text] is close to [Formula: see text]. Next we focus on the planar case and describe the asymptotic profile of some solutions which minimize the energy among functions which are invariant for reflection and rotations of a given angle [Formula: see text]. By considerations based on the Morse index we see that, depending on the values of [Formula: see text] and [Formula: see text], such least energy solutions can be radial, or nonradial and different one from another.
2008 ◽
Vol 15
(1-2)
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pp. 1-23
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2009 ◽
Vol 11
(01)
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pp. 59-69
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2019 ◽
Vol 149
(5)
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pp. 1163-1173