Li Yong-Yong and Li Gui-Dong and Tang Chun-Lei: Ground state sign-changing solutions for critical Choquard equations with steep well potential. (2022)
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Abstract
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.
| Item Type: | Journal |
|---|---|
| Publication full: | Electronic journal of qualitative theory of differential equations |
| Date: | 2022 |
| Number: | 54 |
| ISSN: | 1417-3875 |
| Language: | English |
| DOI: | 10.14232/ejqtde.2022.1.54 |
| Uncontrolled Keywords: | Choquard egyenlet |
| Additional Information: | Bibliogr.: p. 17-20. ; összefoglalás angol nyelven |
| Subjects: | 01. Natural sciences 01. Natural sciences > 01.01. Mathematics |
| Date Deposited: | 2023. Mar. 13. 11:27 |
| Last Modified: | 2023. Mar. 13. 11:27 |
| URI: | http://acta.bibl.u-szeged.hu/id/eprint/78339 |
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