Sign-changing solutions for fractional Schrödinger–Poisson system in ℝ3. Issue 11 (18th August 2019)

• Record Type: Journal Article
• Authors: Guo, Lun
• Is Part Of: Applicable analysis. Volume 98:Issue 11(2019)
• Page Start: 2085
• Page End: 2104
• Publication Date: 2019-08-18
• Subjects: Laplacian -- Schrödinger-Poisson system -- sign-changing solution -- asymptotic behavior; 35J20 -- 35J60; Mathematical analysis -- Periodicals; 515
• DOI: 10.1080/00036811.2018.1448074
• Languages: English
• ISSNs: 0003-6811

Abstract

ABSTRACT: We consider the existence of sign-changing solutions for the following fractional Schrödinger–Poisson system ( - Δ ) s u + V ( x ) u + λ ϕ ( x ) u = f ( u ), & x ∈ R 3, ( - Δ ) t ϕ = u 2, & x ∈ R 3, where s, t ∈ ( 0, 1 ), λ is a positive parameter, V ( x ) : R 3 → R + is a continuous potential function. Since multiple nonlocal terms are involving in the system, some new techniques are applied to prove the existence of a least energy sign-changing solution u λ . Moreover, we prove that the energy of any sign-changing solution to this system is strictly larger than twice of the ground state energy. Furthermore, the asymptotic behavior of u λ as λ → 0 + is also analyzed.