Ground state sign-changing solutions for a class of nonlinear fractional Schrödinger-Poisson system in ℝ³

2017/03/10 by Chao Ji, Ji, Chao
Computer Science · Mathematics · #35J61 #58E30 #Advanced Mathematical Modeling in Engineering #Advanced Mathematical Physics Problems #Analysis of PDEs (math.AP) #FOS: Mathematics #Nonlinear Partial Differential Equations #math.AP #msc:35J61 #msc:58E30

paper · pdf · doi:10.48550/arxiv.1703.03723

arxiv created 2017/03/10 · openalex publication_date 2017/03/10 · arxiv updated 2017/03/13 · openalex created_date 2017/04/07 · openalex updated_date 2026/07/28

Abstract

In this paper, we are concerned with the existence of the least energy sign-changing solutions for the following fractional Schrödinger-Poisson system: \ \beginaligned (-Δ)^s u+V(x)u+λϕ(x)u=f(x, u), in ℝ³,
(-Δ)^tϕ=u², in ℝ³, \endaligned . where λ∈ ℝ⁺ is a parameter, s, t∈ (0, 1) and 4s+2t>3, (-Δ)^s stands for the fractional Laplacian. By constraint variational method and quantitative deformation lemma, we prove that the above problem has one least energy sign-changing solution. Moreover, for any λ>0, we show that the energy of the least energy sign-changing solutions is strictly larger than two times the ground state energy. Finally, we consider λ as a parameter and study the convergence property of the least energy sign-changing solutions as λ\searrow 0.

Citations

• Regularity of the obstacle problem for a fractional power of the laplace operator

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