Open AccessMultiple and least energy sign-changing solutions for Schr¨odinger-Poisson equations in R3 with restraint
Author(s) -
Zhaohong Sun
Publication year - 2017
Publication title -
journal of advances in physics
Language(s) - English
Resource type - Journals
ISSN - 2347-3487
DOI - 10.24297/jap.v13i3.5938
Subject(s) - sign (mathematics) , norm (philosophy) , nonlinear system , invariant (physics) , poisson distribution , energy (signal processing) , mathematics , work (physics) , mathematical analysis , energy method , mathematical physics , physics , pure mathematics , quantum mechanics , statistics , political science , law
In this paper, we study the existence of multiple sign-changing solutions with a prescribed Lp+1−norm and theexistence of least energy sign-changing restrained solutions for the following nonlinear Schr¨odinger-Poisson system:−△u + u + ϕ(x)u = λ|u|p−1u, in R3,−△ϕ(x) = |u|2, in R3.By choosing a proper functional restricted on some appropriate subset to using a method of invariant sets of descending flow,we prove that this system has infinitely many sign-changing solutions with the prescribed Lp+1−norm and has a least energy forsuch sign-changing restrained solution for p ∈ (3, 5). Few existence results of multiple sign-changing restrained solutions areavailable in the literature. Our work generalize some results in literature.