Infinitely many solutions for fractional Schrödinger-Poisson systems with sign-changing potential

Abstract

<p>In this article, we prove the existence of multiple solutions for following fractional Schrödinger-Poisson system with sign-changing potential</p> <pre>(-∆)^su + V(x)u + λφu = ƒ(x, u), x ∈ ℝ³,<br> (-∆)^tφ = u², x ∈ ℝ³,</pre> <p>where (-∆)^α denotes the fractional Laplacian of order α ∈ (0, 1), and the potential V is allowed to be sign-changing. Under certain assumptions on ƒ, we obtain infinitely many solutions for this system.</p>