Article ID | Journal | Published Year | Pages | File Type |
---|---|---|---|---|
7222537 | Nonlinear Analysis: Theory, Methods & Applications | 2018 | 46 Pages |
Abstract
In this paper we study the asymptotic and qualitative properties of least energy radial sign-changing solutions of the fractional Brezis-Nirenberg problem ruled by the s-Laplacian, in a ball of Rn, when sâ(0,1) and n>6s. As usual, λ is the (positive) parameter in the linear part in u. We prove that for λ sufficiently small such solutions cannot vanish at the origin, we show that they change sign at most twice and their zeros coincide with the sign-changes. Moreover, when s is close to 1, such solutions change sign exactly once. Finally we prove that least energy nodal solutions which change sign exactly once have the limit profile of a “tower of bubbles”, as λâ0+, i.e. the positive and negative parts concentrate at the same point with different concentration speeds.
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Authors
G. Cora, A. Iacopetti,