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]).
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