Ground states solutions for some non-autonomous Schrödinger-Bopp-Podolsky system
In this paper we study the existence of ground states solutions for nonautonomous Schrödinger–Bopp–Podolsky system −∆u + u + λK(x)ϕu = b(x)|u| p−2u in R3 −∆ϕ + a 2∆ 2ϕ = 4πK(x)u 2 in R3 where λ > 0, 2 < p ≤ 4 and both K(x) and b(x) are nonnegative functions in R3 Assuming that lim|x|→+∞K(x) =...
Elmentve itt :
| Szerzők: | |
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| Dokumentumtípus: | Folyóirat |
| Megjelent: |
2022
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| Sorozat: | Electronic journal of qualitative theory of differential equations
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| Kulcsszavak: | Schrödinger-Bopp-Podolsky rendszer |
| Tárgyszavak: | |
| doi: | 10.14232/ejqtde.2022.1.51 |
| Online Access: | http://acta.bibl.u-szeged.hu/78336 |
| Tartalmi kivonat: | In this paper we study the existence of ground states solutions for nonautonomous Schrödinger–Bopp–Podolsky system −∆u + u + λK(x)ϕu = b(x)|u| p−2u in R3 −∆ϕ + a 2∆ 2ϕ = 4πK(x)u 2 in R3 where λ > 0, 2 < p ≤ 4 and both K(x) and b(x) are nonnegative functions in R3 Assuming that lim|x|→+∞K(x) = K∞ > 0 and lim|x|→+∞b(x) = b∞ > 0 and satisfying suitable assumptions, but not requiring any symmetry property on them. We show that the existence of a positive solution depends on the parameters λ and p. We also establish the existence of ground state solutions for the case 3.18 ≈ 1+ 73 3 < p ≤ 4. |
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| ISSN: | 1417-3875 |