Multiple Sign-Changing Solutions to Non-local Supercritical Exponent Problem in Symmetric Domains: Non-local Supercritical Exponent Problem: U. Kumar and S. Tiwari.

In this article we establish the existence of a positive solution and multiple sign-changing solutions to the following supercritical exponent problem involving fractional Laplace operator (P b , Ω s) (- Δ) s u = b (x) | u | q - 2 u in Ω , u = 0 on ∂ Ω , where Ω is a bounded smooth domain with non-trivial topology in R N which is invariant under a group G of orthogonal transformations of R N , N ≥ 2 s , s ∈ (0 , 1) , b ∈ C 0 , α (Ω ¯) and positive, q > 2 s ∗ : = 2 N N - 2 s . [ABSTRACT FROM AUTHOR]