On the structure of the nodal set and asymptotics of least energy sign-changing radial solutions of the fractional Brezis–Nirenberg problem. (November 2018) - Cora, G.; Iacopetti, A.
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 R n, when s ∈ ( 0, 1 ) and n > 6 s . 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 λ → 0 +, i.e. the positive and negative parts concentrate at the same point with different concentration speeds.