Nonexistence results of solutions for some fractional $p$-Laplacian equations in $\mathbb{R}^{N}$
In the present paper, we study the nonexistence of nontrivial weak solutions to a class of fractional $p$-Laplacian equation in two cases which are $sp > N$ and $sp < N$. In each of these cases, by using fractional Laplacian theory and inequality techniques, we obtain concrete range of paramet...
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| Format: | Article |
| Language: | English |
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University of Szeged
2024-07-01
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| Series: | Electronic Journal of Qualitative Theory of Differential Equations |
| Subjects: | |
| Online Access: | http://www.math.u-szeged.hu/ejqtde/periodica.html?periodica=1¶mtipus_ertek=publication¶m_ertek=11034 |
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| _version_ | 1841533483299635200 |
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| author | Yuxin Chen Haidong Liu |
| author_facet | Yuxin Chen Haidong Liu |
| author_sort | Yuxin Chen |
| collection | DOAJ |
| description | In the present paper, we study the nonexistence of nontrivial weak solutions to a class of fractional $p$-Laplacian equation in two cases which are $sp > N$ and $sp < N$. In each of these cases, by using fractional Laplacian theory and inequality techniques, we obtain concrete range of parameter for which nontrivial weak solution of the problem does not exist. Our work complements the known nonexistence results in this direction. |
| format | Article |
| id | doaj-art-53cf925c3fdb42feb4bb1ab694e47825 |
| institution | Kabale University |
| issn | 1417-3875 |
| language | English |
| publishDate | 2024-07-01 |
| publisher | University of Szeged |
| record_format | Article |
| series | Electronic Journal of Qualitative Theory of Differential Equations |
| spelling | doaj-art-53cf925c3fdb42feb4bb1ab694e478252025-01-15T21:24:58ZengUniversity of SzegedElectronic Journal of Qualitative Theory of Differential Equations1417-38752024-07-012024341810.14232/ejqtde.2024.1.3411034Nonexistence results of solutions for some fractional $p$-Laplacian equations in $\mathbb{R}^{N}$Yuxin Chen0Haidong LiuQufu Normal University, Qufu, PR ChinaIn the present paper, we study the nonexistence of nontrivial weak solutions to a class of fractional $p$-Laplacian equation in two cases which are $sp > N$ and $sp < N$. In each of these cases, by using fractional Laplacian theory and inequality techniques, we obtain concrete range of parameter for which nontrivial weak solution of the problem does not exist. Our work complements the known nonexistence results in this direction.http://www.math.u-szeged.hu/ejqtde/periodica.html?periodica=1¶mtipus_ertek=publication¶m_ertek=11034fractional $p$-laplacian equationnonexistenceweak solution |
| spellingShingle | Yuxin Chen Haidong Liu Nonexistence results of solutions for some fractional $p$-Laplacian equations in $\mathbb{R}^{N}$ Electronic Journal of Qualitative Theory of Differential Equations fractional $p$-laplacian equation nonexistence weak solution |
| title | Nonexistence results of solutions for some fractional $p$-Laplacian equations in $\mathbb{R}^{N}$ |
| title_full | Nonexistence results of solutions for some fractional $p$-Laplacian equations in $\mathbb{R}^{N}$ |
| title_fullStr | Nonexistence results of solutions for some fractional $p$-Laplacian equations in $\mathbb{R}^{N}$ |
| title_full_unstemmed | Nonexistence results of solutions for some fractional $p$-Laplacian equations in $\mathbb{R}^{N}$ |
| title_short | Nonexistence results of solutions for some fractional $p$-Laplacian equations in $\mathbb{R}^{N}$ |
| title_sort | nonexistence results of solutions for some fractional p laplacian equations in mathbb r n |
| topic | fractional $p$-laplacian equation nonexistence weak solution |
| url | http://www.math.u-szeged.hu/ejqtde/periodica.html?periodica=1¶mtipus_ertek=publication¶m_ertek=11034 |
| work_keys_str_mv | AT yuxinchen nonexistenceresultsofsolutionsforsomefractionalplaplacianequationsinmathbbrn AT haidongliu nonexistenceresultsofsolutionsforsomefractionalplaplacianequationsinmathbbrn |