On the existence of ground state solutions for the logarithmic Schrödinger-Bopp-Podolsky system
This paper deals with the following logarithmic Schrödinger–Bopp–Podolsky system −∆u + V(x)u − ϕu = u log u 2 in R3 2ϕ = 4πu 2 in R3 where V(x) ∈ C(R3 , R). By using the variational method developed by Szulkin for the functional which is the sum of a smooth and a convex lower semicontinuous term, we...
Elmentve itt :
| Szerzők: | |
|---|---|
| Dokumentumtípus: | Folyóirat |
| Megjelent: |
2025
|
| Sorozat: | Electronic journal of qualitative theory of differential equations
|
| Kulcsszavak: | Schrödinger-Bopp-Podolsky rendszer |
| Tárgyszavak: | |
| doi: | 10.14232/ejqtde.2025.1.27 |
| Online Access: | http://acta.bibl.u-szeged.hu/88907 |
| Tartalmi kivonat: | This paper deals with the following logarithmic Schrödinger–Bopp–Podolsky system −∆u + V(x)u − ϕu = u log u 2 in R3 2ϕ = 4πu 2 in R3 where V(x) ∈ C(R3 , R). By using the variational method developed by Szulkin for the functional which is the sum of a smooth and a convex lower semicontinuous term, we study the properties of the solutions for the above system under different potential conditions. When the potential is coercive, we discuss the existence of a ground state solution. Moreover, we also consider the cases where V(x) is periodic or asymptotically periodic, and obtain a ground state solution in each scenario, respectively. |
|---|---|
| Terjedelem/Fizikai jellemzők: | 22 |
| ISSN: | 1417-3875 |