Schrödinger-Poisson systems with singular potential and critical exponent
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In this article we study the Schrödinger-Poisson system
-Δu + V(|x|)u + λφu = ƒ(u), x ∈ ℝ3,
-Δφ = u2, x ∈ ℝ3
where V is a singular potential with the parameter α and the nonlinearity ƒ satisfies critical growth. By applying a generalized version of Lions-type theorem and the Nehari manifold theory, we establish the existence of the nonnegative ground state solution when λ = 0. By the perturbation method, we obtain a nontrivial solution to above system when λ ≠ 0.
CitationLiu, S., Chen, H., & Feng, Z. (2020). Schrödinger-Poisson systems with singular potential and critical exponent. Electronic Journal of Differential Equations, 2020(130), pp. 1-17.
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