@article{e0e5c381bc7b4329b49a21b581ce34b4, title = "Existence of stationary solutions to the Vlasov-Poisson-Boltzmann system", abstract = "In this paper, we study the existence of stationary solutions to the Vlasov-Poisson-Boltzmann system when the background density function tends to a positive constant with a very mild decay rate as | x | → ∞. In fact, the stationary Vlasov-Poisson-Boltzmann system can be written into an elliptic equation with exponential nonlinearity. Under the assumption on the decay rate being (ln (e + | x |))- α for some α > 0, it is shown that this elliptic equation has a unique solution. This result generalizes the previous work [R. Glassey, J. Schaeffer, Y. Zheng, Steady states of the Vlasov-Poisson-Fokker-Planck system, J. Math. Anal. Appl. 202 (1996) 1058-1075] where the decay rate (1 + | x |)- frac(1, 2) is assumed. {\textcopyright} 2006 Elsevier Inc. All rights reserved.", keywords = "Nonlinear elliptic equation, Stationary solutions, Vlasov-Poisson-Boltzmann system", author = "Renjun Duan and Tong Yang and Changjiang Zhu", year = "2007", month = mar, day = "1", doi = "10.1016/j.jmaa.2006.04.047", language = "English", volume = "327", pages = "425--434", journal = "Journal of Mathematical Analysis and Applications", issn = "0022-247X", publisher = "ACADEMIC PRESS INC ELSEVIER SCIENCE", number = "1", }