Existence of non-trivial solutions for fractional Schrödinger-Poisson systems with subcritical growth

Document Type: Special issue editorial

Authors

1 Department of Mathematics, Faculty of Mathematical Sciences, University of Mazandaran, Babolsar, Iran

2 Department of Mathematics, Faculty of Basisc Sciences, Babol(Noshirvani) University of Technology Babol, Iran

10.22075/ijnaa.2019.4393

Abstract

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 the help of the variational methods.

Keywords