Multiplicity of high energy solutions for fractional Schrodinger-Poisson systems with critical frequency
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Date
2022-07-05
Authors
Qu, Siqi
He, Xiaoming
Journal Title
Journal ISSN
Volume Title
Publisher
Texas State University, Department of Mathematics
Abstract
In this article we study the fractional Schrodinger-Poisson system
ɛ2s (-Δ)s u + V(x)u = ϕ|u|2*s - 3u, x ∈ ℝ3,
(-Δ)s ϕ = |u|2*s-1, x ∈ ℝ3,
where s ∈ (1/2, 1), ɛ > 0 is a parameter, 2*s = 6/(3 - 2s) is the critical Sobolev exponent, V ∈ L3/2s (ℝ3) is a nonnegative function which may be zero in some region of ℝ3. By means of variational methods, we present the number of high energy bound states with the topology of the zero set of V for small ɛ.
Description
Keywords
Fractional Schrödinger-Poisson system, High energy solution, Critical Sobolev exponent
Citation
Qu, S., & He, X. (2022). Multiplicity of high energy solutions for fractional Schrodinger-Poisson systems with critical frequency. <i>Electronic Journal of Differential Equations, 2022</i>(47), pp. 1-21.
Rights
Attribution 4.0 International