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Research Article | Open Access

Sign-changing solutions for the Schrödinger-Poisson system with concave-convex nonlinearities in R3

Chen Yang, Chun-Lei Tang( )
School of Mathematics and Statistics, Southwest University, Chongqing, 400715, China
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Abstract

In this paper, we consider the following Schrödinger-Poisson system

{−Δu+V(x)u+ϕu=|u|p−2u+λK(x)|u|q−2uinR3,−Δϕ=u2inR3.

Under the weakly coercive assumption on V and an appropriate condition on K, we investigate the cases when the nonlinearities are of concave-convex type, that is, 1<q<2 and 4<p<6. By constructing a nonempty closed subset of the sign-changing Nehari manifold, we establish the existence of least energy sign-changing solutions provided that λ∈(−∞,λ∗), where λ∗>0 is a constant.

Keywords

Schrödinger-Poisson systemsign-changing solutionsconcave-convex nonlinearitiesvariational method
CLC number: 35A15, 35J20, 35J50

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Communications in Analysis and Mechanics
Volume 15 Issue 4,
November 2023
Pages 638-657
DOI: 10.3934/cam.2023032

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Cite this article:
Yang C, Tang C-L. Sign-changing solutions for the Schrödinger-Poisson system with concave-convex nonlinearities in R3. Communications in Analysis and Mechanics, 2023, 15(4): 638-657. https://doi.org/10.3934/cam.2023032

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Received: 14 September 2023
Revised: 10 October 2023
Accepted: 12 October 2023
Published: 19 October 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)