Abstract and Applied Analysis

Nonexistence Results for the Schrödinger-Poisson Equations with Spherical and Cylindrical Potentials in 3

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

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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.

Article information

Source
Abstr. Appl. Anal., Volume 2013, Special Issue (2013), Article ID 890126, 6 pages.

Dates
First available in Project Euclid: 26 February 2014

Permanent link to this document
https://projecteuclid.org/euclid.aaa/1393443520

Digital Object Identifier
doi:10.1155/2013/890126

Mathematical Reviews number (MathSciNet)
MR3096834

Zentralblatt MATH identifier
07095458

Citation

Jiang, Yongsheng; Zhou, Yanli; Wiwatanapataphee, B.; Ge, Xiangyu. Nonexistence Results for the Schrödinger-Poisson Equations with Spherical and Cylindrical Potentials in ${\Bbb R}^{3}$. Abstr. Appl. Anal. 2013, Special Issue (2013), Article ID 890126, 6 pages. doi:10.1155/2013/890126. https://projecteuclid.org/euclid.aaa/1393443520


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