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- Title
Existence, Nonexistence and Multiplicity Results of a Chern-Simons-Schrödinger System.
- Authors
Xia, Aliang
- Abstract
We study the existence, nonexistence and multiplicity of solutions to Chern-Simons-Schrödinger system { − Δ u + u + λ ( h 2 (| x |) | x | 2 + ∫ | x | + ∞ h (s) s u 2 (s) d s) u = | u | p − 2 u , x ∈ R 2 , u ∈ H r 1 (R 2) , where λ > 0 is a parameter, p ∈ (2 , 4) and h (s) = 1 2 ∫ 0 s r u 2 (r) d r. We prove that the system has no solutions for λ large and has two radial solutions for λ small by studying the decomposition of the Nehari manifold and adapting the fibering method. We also give the qualitative properties about the energy of the solutions and a variational characterization of these extremals values of λ . Our results improve some results in Pomponio and Ruiz (J. Eur. Math. Soc. 17:1463–1486, 2015).
- Subjects
MULTIPLICITY (Mathematics); HAMILTONIAN systems; SCHRODINGER operator; MANIFOLDS (Mathematics); MATHEMATICS
- Publication
Acta Applicandae Mathematicae, 2020, Vol 166, Issue 1, p147
- ISSN
0167-8019
- Publication type
Article
- DOI
10.1007/s10440-019-00260-6