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October 2021 Existence and asymptotic behavior of ground state sign-changing solutions for a nonlinear Schrödinger–Poisson–Kirchhoff system in 3
Mingming Zhang, Aixia Qian
Rocky Mountain J. Math. 51(5): 1879-1897 (October 2021). DOI: 10.1216/rmj.2021.51.1879

Abstract

In this paper, we consider the existence and asymptotic behavior of ground state sign-changing solutions for the following nonlinear Schrödinger–Poisson–Kirchhoff system:

(a+bR3|u|2dx)u+V(x)u+k(x)ϕu=λf(x)u+g(x,u) in 3,ϕ=k(x)u2, in 3.

Under some mild assumptions, by using a series of constructive Nehari manifolds and a quantitative deformation lemma, we prove that the Schrödinger–Poisson–Kirchhoff system possesses at least one ground state sign-changing solution ub for all b>0. Moreover, for any sequence {bn}0+ (n), there exists a subsequence {bnk}, such that {ubnk} converges to u0, where u0 is a sign-changing solution of the equation au+V(x)u=λf(x)u+g(x,u), x3.

Citation

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Mingming Zhang. Aixia Qian. "Existence and asymptotic behavior of ground state sign-changing solutions for a nonlinear Schrödinger–Poisson–Kirchhoff system in 3." Rocky Mountain J. Math. 51 (5) 1879 - 1897, October 2021. https://doi.org/10.1216/rmj.2021.51.1879

Information

Received: 19 October 2020; Accepted: 3 March 2021; Published: October 2021
First available in Project Euclid: 17 February 2022

Digital Object Identifier: 10.1216/rmj.2021.51.1879

Subjects:
Primary: 35J05 , 35J20 , 35J60

Keywords: Brouwer degree theory , ground state , nonlocal term , Schrödinger–Poisson–Kirchhoff system , sign-changing solution

Rights: Copyright © 2021 Rocky Mountain Mathematics Consortium

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Vol.51 • No. 5 • October 2021
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