In this paper, we are concerned with the following fractional Schrödinger-Poisson system:    (−∆s)u + V (x)u + φu = m(x)|u|q−2|u|+ f(x,u), x ∈ Ω, (−∆t)φ = u2, x ∈ Ω, u = φ = 0, x ∈ ∂Ω, where s,t ∈ (0,1], 2t + 4s > 3, 1 < q < 2 and Ω is a bounded smooth domain of R3, and f(x,u) is linearly bounded in u at infinity. Under some assumptions on m, V and f we obtain the existence of non-trivial so...

In this paper, we are concerned with the following fractional Schrödinger-Poisson system:    (−∆s)u + u + λφu = µf(u) +|u|p−2|u|, x ∈R3 (−∆t)φ = u2, x ∈R3 where λ,µ are two parameters, s,t ∈ (0,1] ,2t + 4s > 3 ,1 < p ≤ 2∗ s and f : R → R is continuous function. Using some critical point theorems and truncation technique, we obtain the existence and multiplicity of non-trivial solutions with ...

In this paper, we study the following fractional Schrödinger-poisson systems involving fractional Laplacian operator { (−∆)su+ V (|x|)u+ φ(|x|, u) = f(|x|, u), x ∈ R3, (−∆)tφ = u2, x ∈ R3, (1) where (−∆)s(s ∈ (0, 1)) and (−∆)t(t ∈ (0, 1)) denotes the fractional Laplacian. By variational methods, we obtain the existence of a sequence of radial solutions. c ©2016 All rights reserved.

using the riemann-liouville fractional differintegral operator, the lie theory is reformulated. the fractional poisson bracket over the fractional phase space as 3n state vector is defined to be the fractional lie derivative. its properties are outlined and proved. a theorem for the canonicity of the transformation using the exponential operator is proved. the conservation of its generator is p...

In this paper, we investigate the existence of nontrivial solutions in Bessel Potential space for nonlinearfractional Schrödinger-Poisson system involving distributional Riesz fractional derivative. By using themountain pass theorem combination with perturbation method, prove solutions.