On the structure of the nodal set and asymptotics of least energy sign-changing radial solutions of the fractional Brezis–Nirenberg problem. (November 2018)

• Record Type: Journal Article
• Authors: Cora, G.; Iacopetti, A.
• Is Part Of: Nonlinear analysis. Volume 176(2018)
• Page Start: 226
• Page End: 271
• Publication Date: 2018-11
• Subjects: primary 35J61 35B05 -- secondary 35B33 35B40; Fractional semilinear elliptic equations -- Critical exponent -- Nodal regions -- Sign-changing radial solutions -- Asymptotic behavior; Mathematical analysis -- Periodicals; Functional analysis -- Periodicals; Nonlinear theories -- Periodicals; Analyse mathématique -- Périodiques; Analyse fonctionnelle -- Périodiques; Théories non linéaires -- Périodiques; Functional analysis; Mathematical analysis; Nonlinear theories; Periodicals; Electronic journals; 515.7248
• DOI: 10.1016/j.na.2018.07.001
• Languages: English
• ISSNs: 0362-546X

Abstract

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.