Abstract
In this paper, we show the existence of positive solutions for nonlinear Schrodinger equation with fractional Laplacian(−Δ)su+λu=|u|p−2uinΩ, where Ω⊂RN is an unbounded domain, ∂Ω≠∅ is bounded, λ∈R+, s∈(0,1), N>2s and 2<p<2s⁎. Precisely, we show that the problem has at least one positive solutions. We achieved our results by using variational method together with Brouwer theory of degree. Moreover, we also prove a version to the Fractional operator in unbounded domain of the Global Compactness result due to Struwe (see [24]).
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Disclaimer: 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.