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...
Saved in:
| Main Authors: | , , |
|---|---|
| Format: | Article |
| Language: | English |
| Published: |
AIMS Press
2025-03-01
|
| Series: | Mathematical Modelling and Control |
| Subjects: | |
| Online Access: | https://www.aimspress.com/article/doi/10.3934/mmc.2025001 |
| Tags: |
Add Tag
No Tags, Be the first to tag this record!
|
| _version_ | 1850264542305583104 |
|---|---|
| author | Kexin Ouyang Xinmin Qu Huiqin Lu |
| author_facet | Kexin Ouyang Xinmin Qu Huiqin Lu |
| author_sort | Kexin Ouyang |
| collection | DOAJ |
| description | 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. |
| format | Article |
| id | doaj-art-6b0e1a97552e404aae2b7b6b7f70f50d |
| institution | OA Journals |
| issn | 2767-8946 |
| language | English |
| publishDate | 2025-03-01 |
| publisher | AIMS Press |
| record_format | Article |
| series | Mathematical Modelling and Control |
| spelling | doaj-art-6b0e1a97552e404aae2b7b6b7f70f50d2025-08-20T01:54:41ZengAIMS PressMathematical Modelling and Control2767-89462025-03-015111410.3934/mmc.2025001Sign-changing and signed solutions for fractional Laplacian equations with critical or supercritical nonlinearityKexin Ouyang0Xinmin Qu1Huiqin Lu2School of Mathematics and Statistics, Shandong Normal University, Jinan 250358, ChinaSchool of Mathematics and Statistics, Shandong Normal University, Jinan 250358, ChinaSchool of Mathematics and Statistics, Shandong Normal University, Jinan 250358, ChinaIn 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.https://www.aimspress.com/article/doi/10.3934/mmc.2025001fractional laplacian equationmoser iteration methodtruncation argumentsupercritical growthvariational method |
| spellingShingle | Kexin Ouyang Xinmin Qu Huiqin Lu Sign-changing and signed solutions for fractional Laplacian equations with critical or supercritical nonlinearity Mathematical Modelling and Control fractional laplacian equation moser iteration method truncation argument supercritical growth variational method |
| title | Sign-changing and signed solutions for fractional Laplacian equations with critical or supercritical nonlinearity |
| title_full | Sign-changing and signed solutions for fractional Laplacian equations with critical or supercritical nonlinearity |
| title_fullStr | Sign-changing and signed solutions for fractional Laplacian equations with critical or supercritical nonlinearity |
| title_full_unstemmed | Sign-changing and signed solutions for fractional Laplacian equations with critical or supercritical nonlinearity |
| title_short | Sign-changing and signed solutions for fractional Laplacian equations with critical or supercritical nonlinearity |
| title_sort | sign changing and signed solutions for fractional laplacian equations with critical or supercritical nonlinearity |
| topic | fractional laplacian equation moser iteration method truncation argument supercritical growth variational method |
| url | https://www.aimspress.com/article/doi/10.3934/mmc.2025001 |
| work_keys_str_mv | AT kexinouyang signchangingandsignedsolutionsforfractionallaplacianequationswithcriticalorsupercriticalnonlinearity AT xinminqu signchangingandsignedsolutionsforfractionallaplacianequationswithcriticalorsupercriticalnonlinearity AT huiqinlu signchangingandsignedsolutionsforfractionallaplacianequationswithcriticalorsupercriticalnonlinearity |