Advanced search
Publication Cover
Applicable Analysis
An International Journal
Volume 96, 2017 - Issue 16
Submit an article Journal homepage
160
Views
7
CrossRef citations to date
0
Altmetric
Original Articles

Sharp criteria for the nonlinear Schrödinger equation with combined nonlinearities of power-type and Hartree-type

Lihui LengCollege of Science, Xihua University, Chengdu, China.Correspondence[email protected]
View further author information
,
Xiaoguang LiSichuan Provincial Key Laboratory of Computer Software, Sichuan Normal University, Chengdu, China.View further author information
&
Pengshe ZhengCollege of Science, Xihua University, Chengdu, China.View further author information
Pages 2846-2851 | Received 14 Aug 2016, Accepted 11 Oct 2016, Published online: 27 Oct 2016

References

  • Miao CX, Wu YF, Xu GX. Dynamics for the focusing, energy-critical nonlinear Hartree equation. Forum Math. 2015;27:373–447. doi:10.1515/forum-2011-0087.
  • Ginibre J, Velo G. On a class of Nonlinear Schrödinger equations, the Cauchy problem, general case. J Funct Anal. 1979;32:1–71.
  • Glassey RT. On the blowing up of solutions to the Cauchy problem for nonlinear Schrödinger equations. J Math Phys. 1977;18:1794–1797.
  • Cazenave T. Semilinear Schrödinger equations, Courant lecture notes in mathematics. Vol. 10. New York (NY): NYU, CIMS, AMS; 2003.
  • Holmer J, Roudenko S. A sharp condition for scattering of the radial 3d cubic nonlinear Schrödinger equation. Commun Math Phys. 2008;282:435–467.
  • Merle F, Raphaël P. L2 concentration of blow-up solutions for nonlinear Schrödinger equation with critical nonlinearity. J Differ Equ. 1990;84:205–214.
  • Merle F, Raphaël P. On universality of blow-up profile for L2 critical nonlinear Schrödinger equation. Invent Math. 2004;156:565–572.
  • Ogawa T, Tsutsumi Y. Blow-up of H1 solutions for the nonlinear Schrödinger equation. J Differ Equ. 1991;92:317–330.
  • Zhang J. Sharp conditions of global existence for the nonlinear Schrödinger equations and Klein--Gordon equations. Nonlinear Anal. 2002;48:191–207.
  • Weinstein MI. Nonlinear Schrödinger equations and sharp interpolation estimates. Commun Math Phys. 1983;87:567–576.
  • Fang DY, Han Z. The nonlinear Schrödinger equations with combined nonlinearities of power-type and Hartree-type. Chin Ann Math. 2011;32B:435–474.
  • Zhang J, Zhu SH. Sharp blow-up criteria for the Davey--Stewartson system in R3. Dyn PDE. 2011;8:239–260.
  • Zhu SH. On the Davey--Stewartson system with competing nonlinearities. J Math Phys. 2016;57:031501.
  • Giorgio T. Best constant in sobolev inequality. Ann Mat Pura Appl. 1976;110:353–372.

Reprints and Corporate Permissions

Please note: Selecting permissions does not provide access to the full text of the article, please see our help page How do I view content?

To request a reprint or corporate permissions for this article, please click on the relevant link below:

Order Reprints Request Corporate Permissions

Academic Permissions

Please note: Selecting permissions does not provide access to the full text of the article, please see our help page How do I view content?

Obtain permissions instantly via Rightslink by clicking on the button below:

Request Academic Permissions

If you are unable to obtain permissions via Rightslink, please complete and submit this Permissions form. For more information, please visit our Permissions help page.

Related research

People also read lists articles that other readers of this article have read.

Recommended articles lists articles that we recommend and is powered by our AI driven recommendation engine.

Cited by lists all citing articles based on Crossref citations.
Articles with the Crossref icon will open in a new tab.