On compact and bounded embedding in variable exponent Sobolev spaces and its applications
Abstract For a weighted variable exponent Sobolev space, the compact and bounded embedding results are proved. For that, new boundedness and compact action properties are established for Hardy’s operator and its conjugate in weighted variable exponent Lebesgue spaces. Furthermore, the obtained resul...
| Main Authors: | , , |
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| Format: | Article |
| Language: | English |
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SpringerOpen
2019-09-01
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| Series: | Arabian Journal of Mathematics |
| Subjects: | |
| Online Access: | http://link.springer.com/article/10.1007/s40065-019-00268-8 |
| _version_ | 1818262158778040320 |
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| author | Farman Mamedov Sayali Mammadli Yashar Shukurov |
| author_facet | Farman Mamedov Sayali Mammadli Yashar Shukurov |
| author_sort | Farman Mamedov |
| collection | DOAJ |
| description | Abstract For a weighted variable exponent Sobolev space, the compact and bounded embedding results are proved. For that, new boundedness and compact action properties are established for Hardy’s operator and its conjugate in weighted variable exponent Lebesgue spaces. Furthermore, the obtained results are applied to the existence of positive eigenfunctions for a concrete class of nonlinear ode with nonstandard growth condition. |
| first_indexed | 2024-12-12T18:58:41Z |
| format | Article |
| id | doaj.art-b367f802f370420aba3c05fe60577bfb |
| institution | Directory Open Access Journal |
| issn | 2193-5343 2193-5351 |
| language | English |
| last_indexed | 2024-12-12T18:58:41Z |
| publishDate | 2019-09-01 |
| publisher | SpringerOpen |
| record_format | Article |
| series | Arabian Journal of Mathematics |
| spelling | doaj.art-b367f802f370420aba3c05fe60577bfb2022-12-22T00:15:10ZengSpringerOpenArabian Journal of Mathematics2193-53432193-53512019-09-019240141410.1007/s40065-019-00268-8On compact and bounded embedding in variable exponent Sobolev spaces and its applicationsFarman Mamedov0Sayali Mammadli1Yashar Shukurov2Mathematics and Mechanics Institute of National Academy of SciencesMathematics and Mechanics Institute of National Academy of SciencesMathematics and Mechanics Institute of National Academy of SciencesAbstract For a weighted variable exponent Sobolev space, the compact and bounded embedding results are proved. For that, new boundedness and compact action properties are established for Hardy’s operator and its conjugate in weighted variable exponent Lebesgue spaces. Furthermore, the obtained results are applied to the existence of positive eigenfunctions for a concrete class of nonlinear ode with nonstandard growth condition.http://link.springer.com/article/10.1007/s40065-019-00268-834B1534B1826A4626D10 |
| spellingShingle | Farman Mamedov Sayali Mammadli Yashar Shukurov On compact and bounded embedding in variable exponent Sobolev spaces and its applications Arabian Journal of Mathematics 34B15 34B18 26A46 26D10 |
| title | On compact and bounded embedding in variable exponent Sobolev spaces and its applications |
| title_full | On compact and bounded embedding in variable exponent Sobolev spaces and its applications |
| title_fullStr | On compact and bounded embedding in variable exponent Sobolev spaces and its applications |
| title_full_unstemmed | On compact and bounded embedding in variable exponent Sobolev spaces and its applications |
| title_short | On compact and bounded embedding in variable exponent Sobolev spaces and its applications |
| title_sort | on compact and bounded embedding in variable exponent sobolev spaces and its applications |
| topic | 34B15 34B18 26A46 26D10 |
| url | http://link.springer.com/article/10.1007/s40065-019-00268-8 |
| work_keys_str_mv | AT farmanmamedov oncompactandboundedembeddinginvariableexponentsobolevspacesanditsapplications AT sayalimammadli oncompactandboundedembeddinginvariableexponentsobolevspacesanditsapplications AT yasharshukurov oncompactandboundedembeddinginvariableexponentsobolevspacesanditsapplications |