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Research Article | Open Access

Least energy sign-changing solutions for Kirchhoff-Schrödinger-Poisson system on bounded domains

Xia Su1( )Wen Guan2Xia Li2
Faculty of Mathematics and Physics, Huaiyin Institute of Technology, Huai'an 223003, Jiangsu, China
Department of Applied Mathematics, Lanzhou University of Technology, Lanzhou 730050, Gansu, China
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Abstract

We investigate the following nonlinear system

{ ( a + b Ω | u | 2 d x ) Δ u + ϕ u = λ u + μ | u | 2 u , x Ω , Δ ϕ = u 2 , x Ω , u = ϕ = 0 , x Ω ,

with a , b > 0, λ , μ R , and Ω R 3 is bounded with smooth boundary. Let λ 1 > 0 be the first eigenvalue of ( Δ u , H 0 1 ( Ω ) ). We get that for certain μ ~ > 0 there exists at least one least energy sign-changing solution for the above system if λ < a λ 1 and μ > μ ~ . In addition, we remark that the nonlinearity λ u + μ | u | 2 u does not satisfy the growth conditions.

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Electronic Research Archive
Pages 2959-2973

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Cite this article:
Su X, Guan W, Li X. Least energy sign-changing solutions for Kirchhoff-Schrödinger-Poisson system on bounded domains. Electronic Research Archive, 2023, 31(5): 2959-2973. https://doi.org/10.3934/era.2023149

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Received: 28 October 2022
Revised: 16 February 2023
Accepted: 20 February 2023
Published: 15 May 2023
©2023 the Author(s), licensee AIMS Press.

This is an open access article distributed under the terms of the Creative Commons Attribution License (http://creativecommons.org/licenses/by/4.0)