Ground state sign-changing solutions for critical Choquard equations with steep well potential
In this paper, we study sign-changing solution of the Choquard type equation −∆u + (λV(x) + 1) u = Iα ∗ |u| 2 |u| 2 α−2u + µ|u| p−2u in R N, where N ≥ 3, α ∈ ((N − 4) +, N), Iα is a Riesz potential, p ∈ 2 2N N−2 , 2∗ := N+α N−2 is the upper critical exponent in terms of the Hardy–Littlewood–Sobolev...
Elmentve itt :
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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: | Choquard egyenlet |
| Tárgyszavak: | |
| doi: | 10.14232/ejqtde.2022.1.54 |
| Online Access: | http://acta.bibl.u-szeged.hu/78339 |
| Tartalmi kivonat: | In this paper, we study sign-changing solution of the Choquard type equation −∆u + (λV(x) + 1) u = Iα ∗ |u| 2 |u| 2 α−2u + µ|u| p−2u in R N, where N ≥ 3, α ∈ ((N − 4) +, N), Iα is a Riesz potential, p ∈ 2 2N N−2 , 2∗ := N+α N−2 is the upper critical exponent in terms of the Hardy–Littlewood–Sobolev inequality, µ > 0, λ > 0, V ∈ C(RN, R) is nonnegative and has a potential well. By combining the variational methods and sign-changing Nehari manifold, we prove the existence and some properties of ground state sign-changing solution for λ, µ large enough. Further, we verify the asymptotic behaviour of ground state sign-changing solutions as λ → +∞ and µ → +∞, respectivel. |
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| ISSN: | 1417-3875 |