Positive solutions of Schrödinger-Poisson systems with Hardy potential and indefinite nonlinearity
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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.
CitationLan, Y., Tang, B., & Hu, X. (2020). Positive solutions of Schrodinger-Poisson systems with Hardy potential and indefinite nonlinearity. Electronic Journal of Differential Equations, 2020(47), pp. 1-10.
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