Existence and concentration results for fractional Schrodinger-Poisson system via penalization method
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This article concerns the positive solutions for the fractional Schrödinger-Poisson system
ε2s (-Δ)su + V(x)u + φu = ƒ(u) in ℝ3,
ε2t (-Δ)t φ = u2 in ℝ3,
where ε > 0 is a small parameter, (-Δ)α denotes the fractional Laplacian of orders α = s, t ∈ (3/4, 1), V ∈ C(ℝ3, ℝ) is the potential function and ƒ : ℝ → ℝ is continuous and subcritical. Under a local condition imposed on the potential function, we relate the number of positive solutions with the topology of the set where the potential attains its minimum values. Moreover, we considered some properties of these positive solutions, such as concentration behavior and decay estimate. In the proofs we apply variational methods, penalization techniques and Ljusternik-Schnirelmann theory.
CitationYang, Z., Zhang, W., & Zhao, F. (2021). Existence and concentration results for fractional Schrodinger-Poisson system via penalization method. Electronic Journal of Differential Equations, 2021(14), pp. 1-31.
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