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

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

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...

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Bibliographic Details
Main Authors: Kexin Ouyang, Xinmin Qu, Huiqin Lu
Format: Article
Language:English
Published: AIMS Press 2025-03-01
Series:Mathematical Modelling and Control
Subjects:
fractional laplacian equation
moser iteration method
truncation argument
supercritical growth
variational method
Online Access:https://www.aimspress.com/article/doi/10.3934/mmc.2025001
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Summary: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.
ISSN:2767-8946

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