Ground state for Choquard equation with doubly critical growth nonlinearity
In this paper we consider nonlinear Choquard equation −∆u + V(x)u = (Iα ∗ F(u))f(u) in R N, where V ∈ C(RN), Iα denotes the Riesz potential, f(t) = |t| p−2 t + |t| q−2 t for all t ∈ R, N > 5 and α ∈ (0, N − 4). Under suitable conditions on V, we obtain that the Choquard equation with doubly criti...
Elmentve itt :
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| Dokumentumtípus: | Folyóirat |
| Megjelent: |
2019
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| Sorozat: | Electronic journal of qualitative theory of differential equations
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| Kulcsszavak: | Differenciálegyenlet |
| doi: | 10.14232/ejqtde.2019.1.33 |
| Online Access: | http://acta.bibl.u-szeged.hu/62111 |
| Tartalmi kivonat: | In this paper we consider nonlinear Choquard equation −∆u + V(x)u = (Iα ∗ F(u))f(u) in R N, where V ∈ C(RN), Iα denotes the Riesz potential, f(t) = |t| p−2 t + |t| q−2 t for all t ∈ R, N > 5 and α ∈ (0, N − 4). Under suitable conditions on V, we obtain that the Choquard equation with doubly critical growth nonlinearity, i.e., p = (N + α)/N, q = (N + α)/(N − 2), has a nonnegative ground state solution by variational methods. |
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| Terjedelem/Fizikai jellemzők: | 1-15 |
| ISSN: | 1417-3875 |