Existence and multiplicity results for the fractional Schrodinger-Poisson systems

2015/07/05 by Zhang, Jinguo · 1 citation
Computer Science · Mathematics · #35J20 #47J30 #58E05 #Advanced Mathematical Modeling in Engineering #Advanced Mathematical Physics Problems #Analysis of PDEs (math.AP) #FOS: Mathematics #Functional Analysis (math.FA) #Nonlinear Partial Differential Equations

paper · pdf · doi:10.48550/arxiv.1507.01205

openalex publication_date 2015/07/05 · openalex created_date 2016/06/24 · openalex updated_date 2026/07/28

Abstract

This paper is devoted to study the existence and multiplicity solutions for the nonlinear Schrödinger-Poisson systems involving fractional Laplacian operator: \ \aligned amp;(-Δ)^s u+V(x)u+ ϕu=f(x,u), amp;in ℝ³, amp;(-Δ)^t ϕ=u², amp;in ℝ³, \endaligned . where (-Δ)^α stands for the fractional Laplacian of order α∈ (0 , 1). Under certain assumptions on V and f, we obtain infinitely many high energy solutions for \eqrefeq* without assuming the Ambrosetti-Rabinowitz condition by using the fountain theorem.

Cited by

• Fractional Schrodinger-Poisson Equations With General Nonlinearities

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