Abstract
In this paper, we are concerned with the Schrödinger–Poisson system0.1{−Δu+u+ϕu=|u|p−2uin Rd,Δϕ=u2in Rd.Due to its relevance in physics, the system has been extensively studied and is quite well understood in the case . In contrast, much less information is available in the planar case which is the focus of the present paper. It has been observed by Cingolani S and Weth T (2016 On the planar Schrödinger–Poisson system Ann. Inst. Henri Poincare 33 169–97) that the variational structure of (0.1) differs substantially in the case and leads to a richer structure of the set of solutions. However, the variational approach of Cingolani S and Weth T (2016 On the planar Schrödinger–Poisson system Ann. Inst. Henri Poincare 33 169–97) is restricted to the case which excludes some physically relevant exponents. In the present paper, we remove this unpleasant restriction and explore the more complicated underlying functional geometry in the case with a different variational approach.
Sign-in/Register to access full text options 
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a callDisclaimer: All third-party content on this website/platform is and will remain the property of their respective owners and is provided on "as is" basis without any warranties, express or implied. Use of third-party content does not indicate any affiliation, sponsorship with or endorsement by them. Any references to third-party content is to identify the corresponding services and shall be considered fair use under The CopyrightLaw.
