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2013 Nonexistence Results for the Schrödinger-Poisson Equations with Spherical and Cylindrical Potentials in 3
Yongsheng Jiang, Yanli Zhou, B. Wiwatanapataphee, Xiangyu Ge
Abstr. Appl. Anal. 2013(SI42): 1-6 (2013). DOI: 10.1155/2013/890126

Abstract

We study the following Schrödinger-Poisson system: - Δ u + V ( x ) u + ϕ u = | u | p - 1 u , - Δ ϕ = u 2 , lim | x | + ϕ ( x ) = 0 , where u , ϕ : 3 are positive radial functions, p ( 1 , + ) , x = ( x 1 , x 2 , x 3 ) 3 , and V ( x ) is allowed to take two different forms including V ( x ) = 1 / ( x 1 2 + x 2 2 + x 3 2 ) α / 2 and V ( x ) = 1 / ( x 1 2 + x 2 2 ) 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.

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Yongsheng Jiang. Yanli Zhou. B. Wiwatanapataphee. Xiangyu Ge. "Nonexistence Results for the Schrödinger-Poisson Equations with Spherical and Cylindrical Potentials in 3 ." Abstr. Appl. Anal. 2013 (SI42) 1 - 6, 2013. https://doi.org/10.1155/2013/890126

Information

Published: 2013
First available in Project Euclid: 26 February 2014

zbMATH: 07095458
MathSciNet: MR3096834
Digital Object Identifier: 10.1155/2013/890126

Rights: Copyright © 2013 Hindawi

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Vol.2013 • No. SI42 • 2013
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