Existence of ground state solutions for an asymptotically 2-linear fractional Schrödinger–Poisson system

Abstract

In this paper, we investigate the following fractional Schrödinger-Poisson system: (-) s u + u + φu = f (u), in R 3 , (-) t φ = u 2 , i nR 3 , where 3 4 < s < 1, 1 2 < t < 1, and f is a continuous function, which is superlinear at zero, with f (τ)τ ≥ 3F(τ) ≥ 0, F(τ) = τ 0 f (s) ds, τ ∈ R. We prove that the system admits a ground state solution under the asymptotically 2-linear condition. The result here extends the existing study.

Hyers‐Ulam‐Rassias‐Wright Stability for Fractional Oscillation Equation

“…From the past until now, fractional calculus has gained considerable popularity and importance due to its many applications in various and wide scientific and engineering fields (see [1,2]). We consider the following nonhomogeneous fractional delay oscillation equation:…”