New results concerning a Schrödinger equation involving logarithmic nonlinearity
In this paper, we investigate the existence of ground state solution to a class of Schrödinger equation involving logarithmic nonlinearity. To overcome the lack of smoothness, the corresponding functional $J$ is first decomposed into the sum of a $\mathcal{C}^{1}$ functional and a convex lower semic...
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| Format: | Article |
| Language: | English |
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University of Szeged
2024-12-01
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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=10990 |
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| _version_ | 1846091023580659712 |
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| author | Yaqing Cai Yulin Zhao Chaoliang Luo |
| author_facet | Yaqing Cai Yulin Zhao Chaoliang Luo |
| author_sort | Yaqing Cai |
| collection | DOAJ |
| description | In this paper, we investigate the existence of ground state solution to a class of Schrödinger equation involving logarithmic nonlinearity. To overcome the lack of smoothness, the corresponding functional $J$ is first decomposed into the sum of a $\mathcal{C}^{1}$ functional and a convex lower semicontinuous functional by adapting to the approach of Squassina–Szulkin in [Calc. Var. Partial Differential Equations 54(2015), 585–597]. Secondly, the existence of a ground state solution to the studied equation is proved by using the Mountain Pass Theorem under the weakened Ambrosetti–Rabinowitz conditions. |
| format | Article |
| id | doaj-art-919e8b69a85c4a86a53e0a5055e67b37 |
| 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-919e8b69a85c4a86a53e0a5055e67b372025-01-15T21:24:59ZengUniversity of SzegedElectronic Journal of Qualitative Theory of Differential Equations1417-38752024-12-0120247411610.14232/ejqtde.2024.1.7410990New results concerning a Schrödinger equation involving logarithmic nonlinearityYaqing Cai0Yulin ZhaoChaoliang Luo1School of Science, Hunan University of Technology, Zhuzhou, Hunan, ChinaSchool of Science, Hunan University of Technology, Zhuzhou, Hunan, ChinaIn this paper, we investigate the existence of ground state solution to a class of Schrödinger equation involving logarithmic nonlinearity. To overcome the lack of smoothness, the corresponding functional $J$ is first decomposed into the sum of a $\mathcal{C}^{1}$ functional and a convex lower semicontinuous functional by adapting to the approach of Squassina–Szulkin in [Calc. Var. Partial Differential Equations 54(2015), 585–597]. Secondly, the existence of a ground state solution to the studied equation is proved by using the Mountain Pass Theorem under the weakened Ambrosetti–Rabinowitz conditions.http://www.math.u-szeged.hu/ejqtde/periodica.html?periodica=1¶mtipus_ertek=publication¶m_ertek=10990schrödinger equationsground state solutionlogarithmic nonlinearitymountain pass theorem |
| spellingShingle | Yaqing Cai Yulin Zhao Chaoliang Luo New results concerning a Schrödinger equation involving logarithmic nonlinearity Electronic Journal of Qualitative Theory of Differential Equations schrödinger equations ground state solution logarithmic nonlinearity mountain pass theorem |
| title | New results concerning a Schrödinger equation involving logarithmic nonlinearity |
| title_full | New results concerning a Schrödinger equation involving logarithmic nonlinearity |
| title_fullStr | New results concerning a Schrödinger equation involving logarithmic nonlinearity |
| title_full_unstemmed | New results concerning a Schrödinger equation involving logarithmic nonlinearity |
| title_short | New results concerning a Schrödinger equation involving logarithmic nonlinearity |
| title_sort | new results concerning a schrodinger equation involving logarithmic nonlinearity |
| topic | schrödinger equations ground state solution logarithmic nonlinearity mountain pass theorem |
| url | http://www.math.u-szeged.hu/ejqtde/periodica.html?periodica=1¶mtipus_ertek=publication¶m_ertek=10990 |
| work_keys_str_mv | AT yaqingcai newresultsconcerningaschrodingerequationinvolvinglogarithmicnonlinearity AT yulinzhao newresultsconcerningaschrodingerequationinvolvinglogarithmicnonlinearity AT chaoliangluo newresultsconcerningaschrodingerequationinvolvinglogarithmicnonlinearity |