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by L Martinazzi

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Ali Hyder, Luca Martinazzi
, 2014

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...vature −(2m − 1)! in R2m. One can easily verify that under the assumption (3) Equation (7) has no solutions when m = 1, see e.g. [11, Proposition 6]. On the other hand, when m ≥ 2 we have: Theorem C (=-=[11]-=-) For every m ≥ 2 there is some V > 0 such that Problem (7)-(3) has a radially symmetric solution. Every solution to (7)-(3) (a priori not necessarily radially symmetric) has the asymptotic behavior g...

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unknown authors

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... problem in the last section). Moreover, contrary to [Rob2] and [LS], we do not assume that V0 > 0. In fact, as already discussed in [Mar3], if V0 has changing sign, one can show using the results of =-=[Mar2]-=- that, if (6) holds, blow-up happens only at points where V0 > 0. We also point out that when m = 2, F. Robert [Rob3] proved a version of Theorem 1 where the assumptions (3), (5) and (6) are replaced ...

by
Tianling Jin, Ali Maalaoui, Luca Martinazzi, Jingang Xiong
, 2014

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...hows that Theorem A is sharp as far as V is concerned. Theorem B ([17]). For every non-spherical solution of Problem (4) with n = 4 one has V < |S4|. Surprisingly, it was recently shown by Martinazzi =-=[24]-=- that in dimension n = 6 things are quite different and (4) has solutions for V arbitrarily large. Theorem C ([24]). There exist V∗ > |S6| and V ∗ > 0 such that for every V ∈ (0, V∗] and for every V ≥...

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