Data di Pubblicazione:
2019
Citazione:
Sign-changing bubble-tower solutions to fractional semilinear elliptic problems / G. Cora, A. Iacopetti. - In: DISCRETE AND CONTINUOUS DYNAMICAL SYSTEMS. - ISSN 1078-0947. - 39:10(2019 Oct), pp. 6149-6173. [10.3934/dcds.2019268]
Abstract:
We study the asymptotic and qualitative properties of least energy radial sign- changing solutions to fractional semilinear elliptic problems of the form (−∆)^s u = |u|^{2^*_s−2−ε}u in B_R,
u = 0 in R^n B_R,
where s ∈ (0,1), (−∆)s is the s-Laplacian, BR is a ball of Rn,2^*_s := {2n}/{n-2s} is the critical
Sobolev exponent and ε > 0 is a small parameter. We prove that such solutions have the limit profile of a “tower of bubbles”, as ε → 0+, i.e. the positive and negative parts concentrate at the same point with different concentration speeds. Moreover, we provide information about the nodal set of these solutions.
Tipologia IRIS:
01 - Articolo su periodico
Keywords:
Fractional semilinear elliptic equations; critical exponent; nodal regions; sign-changing radial solutions; asymptotic behavior
Elenco autori:
G. Cora, A. Iacopetti
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