On ground states for the Schrödinger-Poisson system with periodic potentials

Wen Zhang, Jian Zhang () and Xiaoliang Xie
Additional contact information
Wen Zhang: Hunan University of Commerce
Jian Zhang: Hunan University of Commerce
Xiaoliang Xie: Hunan University of Commerce

Indian Journal of Pure and Applied Mathematics, 2016, vol. 47, issue 3, 449-470

Abstract: Abstract This paper is concerned with the following Schrödinger-Poisson system $$\left\{ {\begin{array}{*{20}{c}} { - \Delta u + V\left( x \right)u - K\left( x \right)\phi \left( x \right)u = q\left( x \right){{\left| u \right|}^{p - 2}}u,}&{in\;{\mathbb{R}^3},} \\ { - \Delta \phi = K\left( x \right){u^2},}&{in\;{\mathbb{R}^3},} \end{array}} \right.$$ { − Δ u + V ( x ) u − K ( x ) ϕ ( x ) u = q ( x ) | u | p − 2 u , i n R R 3 , − Δ ϕ = K ( x ) u 2 , i n ℝ 3 , where p ∈ (2, 6), V(x) ∈ C(ℝ3, ℝ) is a general periodic function, K(x) and q(x) are nonperiodic functions. Under suitable assumptions, we prove the existence of ground state solutions via variational methods for strongly indefinite problems.

Keywords: Schrödinger-Poisson system; ground state solutions; variational methods; strongly indefinite functionals (search for similar items in EconPapers)
Date: 2016
References: View complete reference list from CitEc
Citations:

Downloads: (external link)
http://link.springer.com/10.1007/s13226-016-0177-4 Abstract (text/html)
Access to the full text of the articles in this series is restricted.

Related works:
This item may be available elsewhere in EconPapers: Search for items with the same title.

Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text

Persistent link: https://EconPapers.repec.org/RePEc:spr:indpam:v:47:y:2016:i:3:d:10.1007_s13226-016-0177-4

Ordering information: This journal article can be ordered from
https://www.springer.com/journal/13226

DOI: 10.1007/s13226-016-0177-4

Access Statistics for this article

Indian Journal of Pure and Applied Mathematics is currently edited by Nidhi Chandhoke

More articles in Indian Journal of Pure and Applied Mathematics from Springer
Bibliographic data for series maintained by Sonal Shukla () and Springer Nature Abstracting and Indexing ().