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January, 2021 Existence of sign-changing solutions for $p(x)$-Laplacian Kirchhoff type problem in $\mathbb{R}^N$
Zifei SHEN, Bin SHANG, Chenyin QIAN
J. Math. Soc. Japan 73(1): 161-183 (January, 2021). DOI: 10.2969/jmsj/83258325

Abstract

The $p(x)$-Laplacian Kirchhoff type equation involving the nonlocal term $b \int_{\mathbb{R}^N} (1/p(x)) \lvert\nabla u\rvert^{p(x)}dx$ is investigated. Based on the variational methods, deformation lemma and other technique of analysis, it is proved that the problem possesses one least energy sign-changing solution $u_b$ which has precisely two nodal domains. Moreover, the convergence property of $u_b$ as the parameter $b \searrow 0$ is also obtained.

Funding Statement

The research is partly supported by NSFC 11501517, 11671364.

Citation

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Zifei SHEN. Bin SHANG. Chenyin QIAN. "Existence of sign-changing solutions for $p(x)$-Laplacian Kirchhoff type problem in $\mathbb{R}^N$." J. Math. Soc. Japan 73 (1) 161 - 183, January, 2021. https://doi.org/10.2969/jmsj/83258325

Information

Received: 7 September 2019; Published: January, 2021
First available in Project Euclid: 9 September 2020

Digital Object Identifier: 10.2969/jmsj/83258325

Subjects:
Primary: 35J20
Secondary: 35J50, 35J60

Rights: Copyright © 2021 Mathematical Society of Japan

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Vol.73 • No. 1 • January, 2021
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