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In the present paper, it is proved that there are many quasi-periodic solutions of a class of space fractional nonlinear Schrödinger equations with the Riesz fractional derivative by means of KAM (Kolmogorov-Arnold-Moser) theorem. [ABSTRACT FROM AUTHOR]

In this paper, the existence of a nontrivial least energy solution is considered for the nonlinear fractional Schrödinger-Poisson systems (−Δ)su + V(x)u + ϕu = |u|p−1u and (−Δ)tϕ = u2 in R 3 , where (−Δ)α is the fractional Laplacian for α = s, t ∈ (0, 1) with s < t and 2s + 2t > 3. Under some appropriate assumptions on the non-constant potential V(x), we prove the existence of a nontrivial least energy solution when 2 < p < 2 s * − 1 = (3 + 2 s) / (3 − 2 s) by using some new analytical skills and the Nehari-Pohožaev type manifold. [ABSTRACT FROM AUTHOR]