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Existence and mass concentration of pseudo-relativistic Hartree equation.
- Source :
-
Journal of Mathematical Physics . Aug2017, Vol. 58 Issue 8, p1-22. 22p. - Publication Year :
- 2017
-
Abstract
- In this paper, we investigate the constrained minimization problem e(a):=inf{u∊H ∣∣u∣∣22=1}Ea(u), where the energy functional Ea(u) = ∫ℝ3(u√-Δ + m2 u + Vu2)dx-a/2∫ℝ3(∣x∣-1 *u2)u2dx with m∊ℝ, a>0, is defined on a Sobolev space H. We show that there exists a threshold (a* > 0 so that e(a) is achieved if 0<a<a* and has no minimizers if a ⩾a*. We also investigate the asymptotic behavior of non-negative minimizers of e(a) as a→a*. [ABSTRACT FROM AUTHOR]
Details
- Language :
- English
- ISSN :
- 00222488
- Volume :
- 58
- Issue :
- 8
- Database :
- Academic Search Index
- Journal :
- Journal of Mathematical Physics
- Publication Type :
- Academic Journal
- Accession number :
- 124793594
- Full Text :
- https://doi.org/10.1063/1.4996576