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- Title
Multiplicity and concentration of solutions for Choquard equation via Nehari method and pseudo-index theory.
- Authors
Liu, Min; Tang, Zhongwei
- Abstract
This paper concerns the following nonlinear Choquard equation:−ε2Δw + V(x)w = ε−θW(x) (Iθ ∗ (W|w|p))|w|p−2w, x ∈ RN, (∗) where ε > 0, N > 2, Iθ is the Riesz potential with order θ ∈ (0,N), p ∈ [2, N+θ/N−2), min V > 0 and infW > 0. Under proper assumptions, we explore the existence, concentration, convergence and decay estimate of semiclassical solutions for (∗). The multiplicity of solutions is established via pseudo-index theory. The existence of sign-changing solutions is achieved by minimizing the energy on Nehari nodal set.
- Subjects
MULTIPLICITY (Mathematics); NONLINEAR control theory; INDEX theory (Mathematics); PSEUDOSCIENCE; GENERALIZATION
- Publication
Discrete & Continuous Dynamical Systems: Series A, 2019, Vol 39, Issue 6, p3365
- ISSN
1078-0947
- Publication type
Article
- DOI
10.3934/dcds.2019139