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

作者：Jiang, Yongsheng; Zhou, Yanli; Wiwatanapataphee, B.; Ge, Xiangyu^*

来源：Abstract and Applied Analysis, 2013, 2013: 890126.

DOI：10.1155/2013/890126

We study the following Schrodinger-Poisson system: -Delta u + V (x)u + phi u = |u|(P-1)u, -Delta phi = u(2), lim|(x)|(->+infinity)phi(x) = 0, where u,phi : R-3 -> R are positive radial functions, p epsilon (1,+infinity), x = (x(1), x(2), x(3)) epsilon R-3, and V(x) is allowed to take two different forms including V(x) = 1/(x(1)(2) + x(2)(2) + x(3)(2))(alpha/2) and V(x) = 1/(x(1)(2) + x(2)(2))(alpha/2) with alpha > 0. Two theorems for nonexistence of nontrivial solutions are established, giving two regions on the alpha - p plane where the system has no nontrivial solutions.

• 出版日期2013
• 单位中南财经政法大学