Abstract
In this paper, we study equations driven by a non-local integrodifferential operator LK with homogeneous Dirichlet boundary conditions. More precisely, we study the problem {−LKu+V(x)u=|u|p−2u,in Ω,u=0,in RN∖Ω, where 2<p<2s∗=2NN−2s, Ω is an open bounded domain in RN for N⩾2 and V is a L∞ potential such that −LK+V is positive definite. As a particular case, we study the problem {(−Δ)su+V(x)u=|u|p−2u,in Ω,u=0,in RN∖Ω, where (−Δ)s denotes the fractional Laplacian (with 0<s<1). We give assumptions on V, Ω and K such that ground state solutions (resp. least energy nodal solutions) respect the symmetries of some first (resp. second) eigenfunctions of −LK+V, at least for p close to 2. We study the uniqueness, up to a multiplicative factor, of those types of solutions. The results extend those obtained for the local case.
Sign-in/Register to access full text options 
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a callDisclaimer: All third-party content on this website/platform is and will remain the property of their respective owners and is provided on "as is" basis without any warranties, express or implied. Use of third-party content does not indicate any affiliation, sponsorship with or endorsement by them. Any references to third-party content is to identify the corresponding services and shall be considered fair use under The CopyrightLaw.
