Existence Results for Double Phase Problem in Sobolev–Orlicz Spaces with Variable Exponents in Complete Manifold
In this paper, we study the existence of non-negative non-trivial solutions for a class of double-phase problems where the source term is a Caratheodory function that satisfies the Ambrosetti–Rabinowitz type condition in the framework of Sobolev–Orlicz spaces with variable exponents in complete mani...
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| Published in | Mediterranean journal of mathematics Vol. 19; no. 4 |
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| Main Authors | , , , |
| Format | Journal Article |
| Language | English |
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01.08.2022
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| Abstract | In this paper, we study the existence of non-negative non-trivial solutions for a class of double-phase problems where the source term is a Caratheodory function that satisfies the Ambrosetti–Rabinowitz type condition in the framework of Sobolev–Orlicz spaces with variable exponents in complete manifold. Our approach is based on the Nehari manifold and some variational techniques. Furthermore, the Hölder ine-quality, continuous and compact embedding results are proved. |
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| AbstractList | In this paper, we study the existence of non-negative non-trivial solutions for a class of double-phase problems where the source term is a Caratheodory function that satisfies the Ambrosetti–Rabinowitz type condition in the framework of Sobolev–Orlicz spaces with variable exponents in complete manifold. Our approach is based on the Nehari manifold and some variational techniques. Furthermore, the Hölder ine-quality, continuous and compact embedding results are proved. |
| ArticleNumber | 158 |
| Author | Benslimane, Omar Ragusa, Maria Alessandra Bennouna, Jaouad Aberqi, Ahmed |
| Author_xml | – sequence: 1 givenname: Ahmed surname: Aberqi fullname: Aberqi, Ahmed organization: Laboratory LAMA, Sidi Mohamed Ben Abdellah University, National School of Applied Sciences – sequence: 2 givenname: Jaouad surname: Bennouna fullname: Bennouna, Jaouad organization: Laboratory LAMA, Department of Mathematics, Sidi Mohamed Ben Abdellah University, Faculty of Sciences Dhar El Mahraz – sequence: 3 givenname: Omar surname: Benslimane fullname: Benslimane, Omar organization: Laboratory LAMA, Department of Mathematics, Sidi Mohamed Ben Abdellah University, Faculty of Sciences Dhar El Mahraz – sequence: 4 givenname: Maria Alessandra orcidid: 0000-0001-6611-6370 surname: Ragusa fullname: Ragusa, Maria Alessandra email: mariaalessandra.ragusa@unict.it organization: Dipartimento di Matematica e Informatica, Universitá di Catania, RUDN University |
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| Cites_doi | 10.1007/s00605-018-01260-8 10.3390/axioms9030109 10.1515/anona-2020-0022 10.1515/acv-2018-0003 10.1112/S002461070500699X 10.1006/jdeq.1993.1092 10.1006/jmaa.2000.7266 10.1016/j.jde.2018.06.006 10.1080/03605309208820857 10.1007/s12215-020-00577-4 10.1007/978-1-4612-5734-9 10.1080/00036811.2016.1205186 10.1016/j.na.2018.03.016 10.1016/j.jmaa.2020.124423 10.1016/j.jfa.2015.09.008 10.1201/b18601 10.1070/IM1987v029n01ABEH000958 10.1006/jmaa.2000.7617 |
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| Title | Existence Results for Double Phase Problem in Sobolev–Orlicz Spaces with Variable Exponents in Complete Manifold |
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