Ground state sign-changing solutions and infinitely many solutions for fractional logarithmic Schrödinger equations in bounded domains
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| Autore principale: | |
|---|---|
| Data di pubblicazione: | 2021 |
| Altri autori: | , |
| Natura: | Article |
| Lingua: | eng |
| Fonte: | Repositório Institucional da UnB |
| Download full: | https://repositorio.unb.br/handle/10482/45000 https://doi.org/10.14232/ejqtde.2021.1.70 |
Riassunto: | We consider a class of fractional logarithmic Schrödinger equation in bounded domains. First, by means of the constraint variational method, quantitative deformation lemma and some new inequalities, the positive ground state solutions and ground state sign-changing solutions are obtained. These inequalities are derived from the special properties of fractional logarithmic equations and are critical for us to obtain our main results. Moreover, we show that the energy of any sign-changing solution is strictly larger than twice the ground state energy. Finally, we obtain that the equation has infinitely many nontrivial solutions. Our result complements the existing ones to fractional Schrödinger problems when the nonlinearity is sign-changing and satisfies neither the monotonicity condition nor Ambrosetti–Rabinowitz condition. |
| _version_ | 1871442471175585792 |
|---|---|
| author | Tong, Yonghui |
| author2 | Guo, Hui Figueiredo, Giovany de Jesus Malcher |
| author2_role | author author |
| author_browse | Figueiredo, Giovany de Jesus Malcher Guo, Hui Tong, Yonghui |
| author_facet | Tong, Yonghui Guo, Hui Figueiredo, Giovany de Jesus Malcher |
| author_role | author |
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| bitstream.url.fl_str_mv | http://repositorio2.unb.br/jspui/bitstream/10482/45000/1/ARTIGO_GroundStateSign.pdf http://repositorio2.unb.br/jspui/bitstream/10482/45000/2/license.txt |
| collection | Repositório Institucional da UnB |
| dc.contributor.author.fl_str_mv | Tong, Yonghui Guo, Hui Figueiredo, Giovany de Jesus Malcher |
| dc.contributor.email.pt_BR.fl_str_mv | mailto:myyhtong@163.com mailto:huiguo_math@163.com mailto:giovany_ufpa@yahoo.com.br |
| dc.date.accessioned.fl_str_mv | 2022-10-05T18:44:58Z |
| dc.date.available.fl_str_mv | 2022-10-05T18:44:58Z |
| dc.date.issued.fl_str_mv | 2021 |
| dc.identifier.citation.fl_str_mv | TONG, Yonghui; GUO, Hui; FIGUEIREDO, Giovany M. Ground state sign-changing solutions and infinitely many solutions for fractional logarithmic Schrödinger equations in bounded domains. Electronic Journal of Qualitative Theory of Differential Equations, n. 70, 1–14, 2021. DOI 10.14232/ejqtde.2021.1.70. Disponível em: http://www.math.u-szeged.hu/ejqtde/p9311.pdf. Acesso em: 05 out. 2022. |
| dc.identifier.doi.pt_BR.fl_str_mv | https://doi.org/10.14232/ejqtde.2021.1.70 |
| dc.identifier.uri.fl_str_mv | https://repositorio.unb.br/handle/10482/45000 |
| dc.language.iso.fl_str_mv | eng |
| dc.publisher.none.fl_str_mv | University of Szeged |
| dc.rights.driver.fl_str_mv | info:eu-repo/semantics/openAccess |
| dc.source.none.fl_str_mv | reponame:Repositório Institucional da UnB instname:Universidade de Brasília (UnB) instacron:UNB |
| dc.subject.keyword.pt_BR.fl_str_mv | Schrödinger, Equação de Equações diferenciais |
| dc.title.pt_BR.fl_str_mv | Ground state sign-changing solutions and infinitely many solutions for fractional logarithmic Schrödinger equations in bounded domains |
| dc.type.driver.fl_str_mv | info:eu-repo/semantics/article |
| dc.type.status.fl_str_mv | info:eu-repo/semantics/publishedVersion |
| description | We consider a class of fractional logarithmic Schrödinger equation in bounded domains. First, by means of the constraint variational method, quantitative deformation lemma and some new inequalities, the positive ground state solutions and ground state sign-changing solutions are obtained. These inequalities are derived from the special properties of fractional logarithmic equations and are critical for us to obtain our main results. Moreover, we show that the energy of any sign-changing solution is strictly larger than twice the ground state energy. Finally, we obtain that the equation has infinitely many nontrivial solutions. Our result complements the existing ones to fractional Schrödinger problems when the nonlinearity is sign-changing and satisfies neither the monotonicity condition nor Ambrosetti–Rabinowitz condition. |
| eu_rights_str_mv | openAccess |
| format | article |
| id | UNB_b76d09e8dffc2bc742e80f59ba22fc14 |
| identifier_str_mv | TONG, Yonghui; GUO, Hui; FIGUEIREDO, Giovany M. Ground state sign-changing solutions and infinitely many solutions for fractional logarithmic Schrödinger equations in bounded domains. Electronic Journal of Qualitative Theory of Differential Equations, n. 70, 1–14, 2021. DOI 10.14232/ejqtde.2021.1.70. Disponível em: http://www.math.u-szeged.hu/ejqtde/p9311.pdf. Acesso em: 05 out. 2022. |
| instacron_str | UNB |
| institution | UNB |
| instname_str | Universidade de Brasília (UnB) |
| language | eng |
| network_acronym_str | UNB |
| network_name_str | Repositório Institucional da UnB |
| oai_identifier_str | oai:repositorio.unb.br:10482/45000 |
| publishDate | 2021 |
| publishDateSort | 2021 |
| publisher.none.fl_str_mv | University of Szeged |
| reponame_str | Repositório Institucional da UnB |
| repository.mail.fl_str_mv | repositorio@unb.br |
| repository.name.fl_str_mv | Repositório Institucional da UnB - Universidade de Brasília (UnB) |
| repository_id_str | |
| spelling | Tong, YonghuiGuo, HuiFigueiredo, Giovany de Jesus Malchermailto:myyhtong@163.commailto:huiguo_math@163.commailto:giovany_ufpa@yahoo.com.br2022-10-05T18:44:58Z2022-10-05T18:44:58Z2021TONG, Yonghui; GUO, Hui; FIGUEIREDO, Giovany M. Ground state sign-changing solutions and infinitely many solutions for fractional logarithmic Schrödinger equations in bounded domains. Electronic Journal of Qualitative Theory of Differential Equations, n. 70, 1–14, 2021. DOI 10.14232/ejqtde.2021.1.70. Disponível em: http://www.math.u-szeged.hu/ejqtde/p9311.pdf. Acesso em: 05 out. 2022.https://repositorio.unb.br/handle/10482/45000https://doi.org/10.14232/ejqtde.2021.1.70University of SzegedElectronic Journal of Qualitative Theory of Differential Equations - EJQTDE applies the Creative Commons Attribution (CC BY) license to articles and other works we publish. It is to be understood that once a paper is published, it cannot be removed or corrected, although a correction can be published later in the journal and a notation made in the original article telling where a correction appears. Fonte: http://www.math.u-szeged.hu/ejqtde/submit.html. Acesso em: 05 out. 2022.info:eu-repo/semantics/openAccessGround state sign-changing solutions and infinitely many solutions for fractional logarithmic Schrödinger equations in bounded domainsinfo:eu-repo/semantics/publishedVersioninfo:eu-repo/semantics/articleSchrödinger, Equação deEquações diferenciaisWe consider a class of fractional logarithmic Schrödinger equation in bounded domains. First, by means of the constraint variational method, quantitative deformation lemma and some new inequalities, the positive ground state solutions and ground state sign-changing solutions are obtained. These inequalities are derived from the special properties of fractional logarithmic equations and are critical for us to obtain our main results. Moreover, we show that the energy of any sign-changing solution is strictly larger than twice the ground state energy. Finally, we obtain that the equation has infinitely many nontrivial solutions. Our result complements the existing ones to fractional Schrödinger problems when the nonlinearity is sign-changing and satisfies neither the monotonicity condition nor Ambrosetti–Rabinowitz condition.engreponame:Repositório Institucional da UnBinstname:Universidade de Brasília (UnB)instacron:UNBORIGINALARTIGO_GroundStateSign.pdfARTIGO_GroundStateSign.pdfapplication/pdf517945http://repositorio2.unb.br/jspui/bitstream/10482/45000/1/ARTIGO_GroundStateSign.pdffec8fd22a37a6472d6ec03e62786e276MD51open accessLICENSElicense.txtlicense.txttext/plain163http://repositorio2.unb.br/jspui/bitstream/10482/45000/2/license.txtba54f8d1c5f5ec8df897ad678916c701MD52open access10482/450002023-05-26 21:16:56.216open accessoai:repositorio.unb.br:10482/45000U3VibWlzc8OjbyBlZmV0aXZhZGEgcG9yIGludGVncmFudGUgZGEgZXF1aXBlIGRvIFJlcG9zaXTDs3JpbyBJbnN0aXR1Y2lvbmFsIGRhIFVuQiBkZSBhY29yZG8gY29tIGxpY2Vuw6dhIGNvbmNlZGlkYSBwZWxvIGF1dG9yIGUvb3UgZGV0ZW50b3IgZG9zIGRpcmVpdG9zIGF1dG9yYWlzLg==Repositório InstitucionalPUBhttps://repositorio.unb.br/oai/requestrepositorio@unb.bropendoar:2023-05-27T00:16:56Repositório Institucional da UnB - Universidade de Brasília (UnB) |
| spellingShingle | Ground state sign-changing solutions and infinitely many solutions for fractional logarithmic Schrödinger equations in bounded domains Tong, Yonghui Schrödinger, Equação de Equações diferenciais |
| status_str | publishedVersion |
| title | Ground state sign-changing solutions and infinitely many solutions for fractional logarithmic Schrödinger equations in bounded domains |
| title_full | Ground state sign-changing solutions and infinitely many solutions for fractional logarithmic Schrödinger equations in bounded domains |
| title_fullStr | Ground state sign-changing solutions and infinitely many solutions for fractional logarithmic Schrödinger equations in bounded domains |
| title_full_unstemmed | Ground state sign-changing solutions and infinitely many solutions for fractional logarithmic Schrödinger equations in bounded domains |
| title_short | Ground state sign-changing solutions and infinitely many solutions for fractional logarithmic Schrödinger equations in bounded domains |
| title_sort | Ground state sign-changing solutions and infinitely many solutions for fractional logarithmic Schrödinger equations in bounded domains |
| topic | Schrödinger, Equação de Equações diferenciais |
| url | https://repositorio.unb.br/handle/10482/45000 https://doi.org/10.14232/ejqtde.2021.1.70 |