Quasilinear Schrödinger equations with general sublinear conditions
In this paper, we study the quasilinear Schrödinger equations $$-\Delta u+V(x)u+\Delta(u^2)u = f(x, u),\qquad\forall x\in\mathbb{R}^N,$$ where $V\in C(\mathbb{R}^N;\mathbb{R})$ may change sign and $f$ is only locally defined for $|u|$ small. Under some new assumptions on $V$ and $f$, we show that th...
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University of Szeged
2024-12-01
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| Series: | Electronic Journal of Qualitative Theory of Differential Equations |
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| Online Access: | http://www.math.u-szeged.hu/ejqtde/periodica.html?periodica=1¶mtipus_ertek=publication¶m_ertek=11196 |
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| author | Safa Bridaa Abderrazek Hassine Taib Talbi |
| author_facet | Safa Bridaa Abderrazek Hassine Taib Talbi |
| author_sort | Safa Bridaa |
| collection | DOAJ |
| description | In this paper, we study the quasilinear Schrödinger equations $$-\Delta u+V(x)u+\Delta(u^2)u = f(x, u),\qquad\forall x\in\mathbb{R}^N,$$ where $V\in C(\mathbb{R}^N;\mathbb{R})$ may change sign and $f$ is only locally defined for $|u|$ small. Under some new assumptions on $V$ and $f$, we show that the above equation has a sequence of solutions converging to zero. Some recent results in the literature are generalized and significantly improved and some examples are also given to illustrate our main theoretical results. |
| format | Article |
| id | doaj-art-18e9e9c0e3e247a7804dcb79f5c5161b |
| institution | Kabale University |
| issn | 1417-3875 |
| language | English |
| publishDate | 2024-12-01 |
| publisher | University of Szeged |
| record_format | Article |
| series | Electronic Journal of Qualitative Theory of Differential Equations |
| spelling | doaj-art-18e9e9c0e3e247a7804dcb79f5c5161b2025-01-15T21:24:59ZengUniversity of SzegedElectronic Journal of Qualitative Theory of Differential Equations1417-38752024-12-0120247311910.14232/ejqtde.2024.1.7311196Quasilinear Schrödinger equations with general sublinear conditionsSafa Bridaa0https://orcid.org/0009-0002-8345-7657Abderrazek Hassinehttps://orcid.org/0000-0003-1233-2574Taib Talbi1https://orcid.org/0000-0003-2066-769XHigher Institute of Applied Sciences and Technology of Kairouan, Kairouan, TunisiaHigher Institute of Science Computer and Mathematics Monastir, TunisiaIn this paper, we study the quasilinear Schrödinger equations $$-\Delta u+V(x)u+\Delta(u^2)u = f(x, u),\qquad\forall x\in\mathbb{R}^N,$$ where $V\in C(\mathbb{R}^N;\mathbb{R})$ may change sign and $f$ is only locally defined for $|u|$ small. Under some new assumptions on $V$ and $f$, we show that the above equation has a sequence of solutions converging to zero. Some recent results in the literature are generalized and significantly improved and some examples are also given to illustrate our main theoretical results.http://www.math.u-szeged.hu/ejqtde/periodica.html?periodica=1¶mtipus_ertek=publication¶m_ertek=11196variational methodscritical pointsquasilinear schrödinger equations |
| spellingShingle | Safa Bridaa Abderrazek Hassine Taib Talbi Quasilinear Schrödinger equations with general sublinear conditions Electronic Journal of Qualitative Theory of Differential Equations variational methods critical points quasilinear schrödinger equations |
| title | Quasilinear Schrödinger equations with general sublinear conditions |
| title_full | Quasilinear Schrödinger equations with general sublinear conditions |
| title_fullStr | Quasilinear Schrödinger equations with general sublinear conditions |
| title_full_unstemmed | Quasilinear Schrödinger equations with general sublinear conditions |
| title_short | Quasilinear Schrödinger equations with general sublinear conditions |
| title_sort | quasilinear schrodinger equations with general sublinear conditions |
| topic | variational methods critical points quasilinear schrödinger equations |
| url | http://www.math.u-szeged.hu/ejqtde/periodica.html?periodica=1¶mtipus_ertek=publication¶m_ertek=11196 |
| work_keys_str_mv | AT safabridaa quasilinearschrodingerequationswithgeneralsublinearconditions AT abderrazekhassine quasilinearschrodingerequationswithgeneralsublinearconditions AT taibtalbi quasilinearschrodingerequationswithgeneralsublinearconditions |