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Least energy solutions for a class of fractional Schrödinger-Poisson systems.
- Source :
-
Journal of Mathematical Physics . Aug2018, Vol. 59 Issue 8, pN.PAG-N.PAG. 21p. - Publication Year :
- 2018
-
Abstract
- In this paper, the existence of a nontrivial least energy solution is considered for the nonlinear fractional Schrödinger-Poisson systems (−Δ)su + V(x)u + ϕu = |u|p−1u and (−Δ)tϕ = u2 in R 3 , where (−Δ)α is the fractional Laplacian for α = s, t ∈ (0, 1) with s < t and 2s + 2t > 3. Under some appropriate assumptions on the non-constant potential V(x), we prove the existence of a nontrivial least energy solution when 2 < p < 2 s * − 1 = (3 + 2 s) / (3 − 2 s) by using some new analytical skills and the Nehari-Pohožaev type manifold. [ABSTRACT FROM AUTHOR]
Details
- Language :
- English
- ISSN :
- 00222488
- Volume :
- 59
- Issue :
- 8
- Database :
- Academic Search Index
- Journal :
- Journal of Mathematical Physics
- Publication Type :
- Academic Journal
- Accession number :
- 131587720
- Full Text :
- https://doi.org/10.1063/1.5047663