Positive solutions of Schrödinger-Poisson systems with Hardy potential and indefinite nonlinearity
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Date
2020-05-21
Authors
Lan, Yongyi
Tang, Biyun
Hu, Xian
Journal Title
Journal ISSN
Volume Title
Publisher
Texas State University, Department of Mathematics
Abstract
In this article, we study the nonlinear Schrödinger-Poisson system
-Δu + u - μ u/|x|2 + l(x)φu = k(x)|u|p-2u x ∈ ℝ3,
-Δφ = l(x)u2 x ∈ ℝ3,
where k ∈ C(ℝ3) and 4 < p < 6, k changes sign in ℝ3 and lim sup|x|→∞ k(x) = k∞ < 0. We prove that Schrödinger-Poisson systems with Hardy potential and indefinite nonlinearity have at least one positive solution, using variational methods.
Description
Keywords
Hardy potential, Variational methods, Indefinite nonlinearity, Positive solution
Citation
Lan, Y., Tang, B., & Hu, X. (2020). Positive solutions of Schrodinger-Poisson systems with Hardy potential and indefinite nonlinearity. <i>Electronic Journal of Differential Equations, 2020</i>(47), pp. 1-10.
Rights
Attribution 4.0 International