Multiple Solutions for a Class of Fractional Schrödinger-Poisson System
نویسندگان
چکیده
منابع مشابه
On a class of nonlinear fractional Schrödinger-Poisson systems
In this paper, we are concerned with the following fractional Schrödinger-Poisson system: (−∆s)u + V (x)u + φu = m(x)|u|q−2|u|+ f(x,u), x ∈ Ω, (−∆t)φ = u2, x ∈ Ω, u = φ = 0, x ∈ ∂Ω, where s,t ∈ (0,1], 2t + 4s > 3, 1 < q < 2 and Ω is a bounded smooth domain of R3, and f(x,u) is linearly bounded in u at infinity. Under some assumptions on m, V and f we obtain the existence of non-trivial so...
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In this paper, we are concerned with the following fractional Schrödinger-Poisson system: (−∆s)u + u + λφu = µf(u) +|u|p−2|u|, x ∈R3 (−∆t)φ = u2, x ∈R3 where λ,µ are two parameters, s,t ∈ (0,1] ,2t + 4s > 3 ,1 < p ≤ 2∗ s and f : R → R is continuous function. Using some critical point theorems and truncation technique, we obtain the existence and multiplicity of non-trivial solutions with ...
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and Applied Analysis 3 Definition 2.2 see 8 . Let f t be a function defined on a, b . The left and right RiemannLiouville fractional derivatives of order τ for function f t denoted by aDτbf t and tD τ bf t , respectively, are defined by aD τ t f t d dtn aD τ−n t f t 1 Γ n − τ d dtn (∫ t a t − s n−τ−1f s ds ) , tD τ bf t −1 n d dtn tD τ−n b f t 1 Γ n − τ d dtn (∫b t t − s n−τ−1f s ds ) , 2.2 whe...
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In this paper, under appropriate oscillating behaviours of the nonlinear term, we prove some multiplicity results for a class of nonlinear fractional equations. These problems have a variational structure and we find three solutions for them by exploiting an abstract result for smooth functionals defined on a reflexive Banach space. To make the nonlinear methods work, some careful analysis of t...
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ژورنال
عنوان ژورنال: Journal of Function Spaces
سال: 2019
ISSN: 2314-8896,2314-8888
DOI: 10.1155/2019/8981528