Sign-changing bubble-tower solutions to fractional semilinear elliptic problems

Abstract

We study the asymptotic and qualitative properties of least energy radial signchanging solutions to fractional semilinear elliptic problems of the formn−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.