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 C 1 functional and a convex lower semicontinuous functi...
Elmentve itt :
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| Dokumentumtípus: | Folyóirat |
| Megjelent: |
2024
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| Sorozat: | Electronic journal of qualitative theory of differential equations
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| Kulcsszavak: | Schrödinger-egyenlet, Mountain Pass tétel |
| Tárgyszavak: | |
| doi: | 10.14232/ejqtde.2024.1.74 |
| Online Access: | http://acta.bibl.u-szeged.hu/88876 |
| Tartalmi kivonat: | 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 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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| Terjedelem/Fizikai jellemzők: | 16 |
| ISSN: | 1417-3875 |