Nonexistence Results for the Schrödinger‐Poisson Equations with Spherical and Cylindrical Potentials in ℝ3

Yongsheng Jiang, Yanli Zhou, B. Wiwatanapataphee and Xiangyu Ge

Abstract and Applied Analysis, 2013, vol. 2013, issue 1

Abstract: We study the following Schrödinger‐Poisson system: −Δu + V(x)u + ϕu = |u|p−1u, −Δϕ = u2, lim|x|→+∞ϕ(x) = 0, where u, ϕ : ℝ3 → ℝ are positive radial functions, p ∈ (1, +∞), x = (x1, x2, x3) ∈ ℝ3, and V(x) is allowed to take two different forms including V(x)=1/(x12+x22+x32) α/2 and V(x)=1/(x12+x22) α/2 with α > 0. Two theorems for nonexistence of nontrivial solutions are established, giving two regions on the α − p plane where the system has no nontrivial solutions.

Date: 2013
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https://doi.org/10.1155/2013/890126

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Persistent link: https://EconPapers.repec.org/RePEc:wly:jnlaaa:v:2013:y:2013:i:1:n:890126

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