Sign-changing and signed solutions for fractional Laplacian equations with critical or supercritical nonlinearity

Kexin Ouyang; Xinmin Qu; Huiqin Lu; Kexin Ouyang; Xinmin Qu; Huiqin Lu

doi:10.3934/mmc.2025001

Mathematical Modelling and Control

2025, Volume 5, Issue 1: 1-14. doi: 10.3934/mmc.2025001

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Sign-changing and signed solutions for fractional Laplacian equations with critical or supercritical nonlinearity

1.
School of Mathematics and Statistics, Shandong Normal University, Jinan 250358, China
2.
Mathematics and Science College, Shanghai Normal University, Shanghai 200234, China

Received: 17 December 2022 Revised: 22 April 2023 Accepted: 20 June 2023 Published: 05 March 2025

In this paper, we investigate the existence of sign-changing and signed solutions for nonlinear elliptic equations driven by nonlocal integro-differential operators with critical or supercritical nonlinearity. By combining an appropriate truncation argument with a constrained minimization method and the Moser iteration method, we obtain a sign-changing solution and a signed solution for them under some suitable assumptions. As a particular case, we drive an existence theorem of sign-changing and signed solutions for the fractional Laplacian equations with critical or supercritical growth.
- fractional Laplacian equation,
- Moser iteration method,
- truncation argument,
- supercritical growth,
- variational method
Citation: Kexin Ouyang, Xinmin Qu, Huiqin Lu. Sign-changing and signed solutions for fractional Laplacian equations with critical or supercritical nonlinearity[J]. Mathematical Modelling and Control, 2025, 5(1): 1-14. doi: 10.3934/mmc.2025001

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Abstract

In this paper, we investigate the existence of sign-changing and signed solutions for nonlinear elliptic equations driven by nonlocal integro-differential operators with critical or supercritical nonlinearity. By combining an appropriate truncation argument with a constrained minimization method and the Moser iteration method, we obtain a sign-changing solution and a signed solution for them under some suitable assumptions. As a particular case, we drive an existence theorem of sign-changing and signed solutions for the fractional Laplacian equations with critical or supercritical growth.

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