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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| Main Authors: | , , |
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| Format: | Article |
| Language: | English |
| Published: |
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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| Summary: | 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. |
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| ISSN: | 1417-3875 |