Least energy sign-changing solutions for a class of fractional Kirchhoff–Poisson system

2021 ◽  
Vol 62 (9) ◽  
pp. 091508
Author(s):  
Yuxi Meng ◽  
Xingrui Zhang ◽  
Xiaoming He
Keyword(s):  
Poisson System ◽  
Sign Changing Solutions ◽  
Least Energy

scholarly journals The Existence of the Sign-Changing Solutions for the Kirchhoff-Schrödinger-Poisson System in Bounded Domains

2020 ◽  
Vol 2020 ◽  
pp. 1-10
Author(s):  
Cun-bin An ◽  
Jiangyan Yao ◽  
Wei Han
Keyword(s):  
Existence Result ◽  
Degree Theory ◽  
Bounded Domains ◽  
Poisson System ◽  
Convergence Properties ◽  
Doubling Property ◽  
Deformation Lemma ◽  
Quantitative Deformation Lemma ◽  
Sign Changing Solutions ◽  
Least Energy

In this paper, we study a class of the Kirchhoff-Schrödinger-Poisson system. By using the quantitative deformation lemma and degree theory, the existence result of the least energy sign-changing solution u0 is obtained. Meanwhile, the energy doubling property is proved, that is, we prove that the energy of any sign-changing solution is strictly larger than twice that of the least energy. Moreover, we also get the convergence properties of u0 as the parameters b↘0 and λ↘0.

scholarly journals Multiple and least energy sign-changing solutions for Schr¨odinger-Poisson equations in R3 with restraint

2017 ◽  
Vol 13 (3) ◽  
pp. 4763-4778
Author(s):  
Zhaohong Sun
Keyword(s):  
Existence Results ◽  
Invariant Sets ◽  
Poisson Equations ◽  
Sign Changing Solutions ◽  
Least Energy

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.

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