Ground state sign-changing solutions for critical Choquard equations with steep well potential

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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