We found a match
Your institution may have access to this item. Find your institution then sign in to continue.
- Title
Multiple solutions for critical Choquard-Kirchhoff type equations.
- Authors
Liang, Sihua; Pucci, Patrizia; Zhang, Binlin
- Abstract
In this article, we investigate multiplicity results for Choquard-Kirchhoff type equations, with Hardy-Littlewood-Sobolev critical exponents, − (a + b ∫RN |∇u|2dx) Δu = αk(x)|u|q−2u + β (∫RN |u(y)|2*μ/|x−y|μ dy) |u|2*μ−2u, x ∈ RN, where a > 0, b ≥ 0, 0 < μ < N, N ≥ 3, α and β are positive real parameters, 2*μ = (2 N − μ) / (N − 2) is the critical exponent in the sense of Hardy-Littlewood-Sobolev inequality, k ∈ Lr(ℝN), with r = 2∗/(2∗ − q) if 1 < q < 2* and r = ∞ if q ≥ 2∗. According to the different range of q, we discuss the multiplicity of solutions to the above equation, using variational methods under suitable conditions. In order to overcome the lack of compactness, we appeal to the concentration compactness principle in the Choquard-type setting.
- Subjects
EQUATIONS; CRITICAL exponents; MULTIPLICITY (Mathematics)
- Publication
Advances in Nonlinear Analysis, 2021, Vol 10, Issue 1, p400
- ISSN
2191-9496
- Publication type
Article
- DOI
10.1515/anona-2020-0119