Asymptotic behaviour of ground state solutions for the fractional Henon equation

作者：Chen, Haixia; Xu, Xiaolin; Yang, Xiaolong^*

来源：Journal of Mathematical Analysis and Applications, 2022, 505(1): 125456.

DOI：10.1016/j.jmaa.2021.125456

• Asymptotic behaviour
• Ground state solution
• Fractional Henon equation

This paper is concerned with the following fractional Henon equation @@@ {(-Delta)(s)u = |x|(alpha)u(p-1), x is an element of Omega, @@@ u > 0, x is an element of Omega, @@@ u = 0, x is an element of R-N \Omega, @@@ Where s is an element of (0, 1), N > 2s, alpha > 0 and Omega subset of R-N is a bounded domain with the origin and smooth boundary, we consider the limiting behaviour of the ground state solution up as p -> 2*(s) = 2N/(N - 2s). Moreover, we prove that up concentrates at the point farthest from the origin on the boundary of Omega. This work can be seen as a nonlocal analogue of the results of Cao and Peng [8].