Positive Solutions for Perturbed Fractional <i>p</i>-Laplacian Problems
In this article, we consider a class of quasilinear elliptic equations involving the fractional <i>p</i>-Laplacian, in which the nonlinear term satisfies subcritical or critical growth. Based on a fixed point result due to Carl and Heikkilä, we can well overcome the lack of compactness w...
| Main Authors: | , |
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| Format: | Article |
| Language: | English |
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MDPI AG
2022-10-01
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| Series: | Fractal and Fractional |
| Subjects: | |
| Online Access: | https://www.mdpi.com/2504-3110/6/10/571 |
| _version_ | 1827650209299038208 |
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| author | Mengfei Tao Binlin Zhang |
| author_facet | Mengfei Tao Binlin Zhang |
| author_sort | Mengfei Tao |
| collection | DOAJ |
| description | In this article, we consider a class of quasilinear elliptic equations involving the fractional <i>p</i>-Laplacian, in which the nonlinear term satisfies subcritical or critical growth. Based on a fixed point result due to Carl and Heikkilä, we can well overcome the lack of compactness which has been a key difficulty for elliptic equations with critical growth. Moreover, we establish the existence and boundedness of the weak solutions for the above equations. |
| first_indexed | 2024-03-09T20:12:12Z |
| format | Article |
| id | doaj.art-fade2bb59c9144629059db9ece884be8 |
| institution | Directory Open Access Journal |
| issn | 2504-3110 |
| language | English |
| last_indexed | 2024-03-09T20:12:12Z |
| publishDate | 2022-10-01 |
| publisher | MDPI AG |
| record_format | Article |
| series | Fractal and Fractional |
| spelling | doaj.art-fade2bb59c9144629059db9ece884be82023-11-24T00:11:49ZengMDPI AGFractal and Fractional2504-31102022-10-0161057110.3390/fractalfract6100571Positive Solutions for Perturbed Fractional <i>p</i>-Laplacian ProblemsMengfei Tao0Binlin Zhang1College of Mathematics and Systems Science, Shandong University of Science and Technology, Qingdao 266590, ChinaCollege of Mathematics and Systems Science, Shandong University of Science and Technology, Qingdao 266590, ChinaIn this article, we consider a class of quasilinear elliptic equations involving the fractional <i>p</i>-Laplacian, in which the nonlinear term satisfies subcritical or critical growth. Based on a fixed point result due to Carl and Heikkilä, we can well overcome the lack of compactness which has been a key difficulty for elliptic equations with critical growth. Moreover, we establish the existence and boundedness of the weak solutions for the above equations.https://www.mdpi.com/2504-3110/6/10/571fractional p-Laplaciancritical growthfixed point theorem |
| spellingShingle | Mengfei Tao Binlin Zhang Positive Solutions for Perturbed Fractional <i>p</i>-Laplacian Problems Fractal and Fractional fractional p-Laplacian critical growth fixed point theorem |
| title | Positive Solutions for Perturbed Fractional <i>p</i>-Laplacian Problems |
| title_full | Positive Solutions for Perturbed Fractional <i>p</i>-Laplacian Problems |
| title_fullStr | Positive Solutions for Perturbed Fractional <i>p</i>-Laplacian Problems |
| title_full_unstemmed | Positive Solutions for Perturbed Fractional <i>p</i>-Laplacian Problems |
| title_short | Positive Solutions for Perturbed Fractional <i>p</i>-Laplacian Problems |
| title_sort | positive solutions for perturbed fractional i p i laplacian problems |
| topic | fractional p-Laplacian critical growth fixed point theorem |
| url | https://www.mdpi.com/2504-3110/6/10/571 |
| work_keys_str_mv | AT mengfeitao positivesolutionsforperturbedfractionalipilaplacianproblems AT binlinzhang positivesolutionsforperturbedfractionalipilaplacianproblems |