For the 3D focusing cubic nonlinear SchrSdinger equation, scattering of H1 solutions inside the （scale invariant） potential well was established by Holmer and Roudenko （radial case） and Duyckaerts et al. （general...For the 3D focusing cubic nonlinear SchrSdinger equation, scattering of H1 solutions inside the （scale invariant） potential well was established by Holmer and Roudenko （radial case） and Duyckaerts et al. （general case） in 2008. In this paper, we extend this result to arbitrary space dimensions and focusing, mass-supercritical and energy-subcritical power nonlinearities, by adapting the method of Duyckaerts et al.展开更多
In this paper, we consider the nonlinear fractional Schr6dinger equations with Hartree type nonlin- earity in mass-supercritical and energy-subcritical case. Pohozaev identity, we established a threshold condition spa...In this paper, we consider the nonlinear fractional Schr6dinger equations with Hartree type nonlin- earity in mass-supercritical and energy-subcritical case. Pohozaev identity, we established a threshold condition space. By sharp Hardy-Littlewood-Sobolev inequality and the which leads to a global existence of solutions in energy展开更多
We investigate the nonlinear Schrdinger equation iut＋△u＋｜u｜^p-1u = 0 with 1＋4/N 〈 p 〈 1＋4/（N-2）（when N = 1,2,1 ＋4/N 〈 p 〈 ∞） in energy space H^1 and study the divergent property of infinite-variance a...We investigate the nonlinear Schrdinger equation iut＋△u＋｜u｜^p-1u = 0 with 1＋4/N 〈 p 〈 1＋4/（N-2）（when N = 1,2,1 ＋4/N 〈 p 〈 ∞） in energy space H^1 and study the divergent property of infinite-variance and nonradial solutions.If M（u）^（1-sc）/sc E（u） 〈 M（Q）^（1-sc）/scE（Q） and ｜｜u0｜｜0^（1-sc）/sc ｜｜▽u0｜｜2 〉 ｜｜Q｜｜^（1-sc）/sc ｜▽Q｜｜2,then either u（t） blows up in finite forward time or u（t） exists globally for positive time and there exists a time sequence tn→ ＋∞ such that ｜｜ ▽u（tn）｜｜2 →＋∞.Here Q is the ground state solution of —（1 — sc）Q ＋ △Q ＋ ｜Q｜p-1Q = 0.A similar result holds for negative time.This extend the result of the 3D cubic Schrodinger equation obtained by Holmer to the general mass-supercritical and energy-subcritical case.展开更多
基金supported by National Natural Science Foundation of China (Grants Nos. 10871175, 10931007)Zhejiang Natural Science Foundation (Grants No. Z6100217)Zhejiang University's Pao Yu-Kong International Fund
文摘For the 3D focusing cubic nonlinear SchrSdinger equation, scattering of H1 solutions inside the （scale invariant） potential well was established by Holmer and Roudenko （radial case） and Duyckaerts et al. （general case） in 2008. In this paper, we extend this result to arbitrary space dimensions and focusing, mass-supercritical and energy-subcritical power nonlinearities, by adapting the method of Duyckaerts et al.
基金Supported by the National Center of Mathematics and Interdisciplinary Sciences,CAS
文摘In this paper, we consider the nonlinear fractional Schr6dinger equations with Hartree type nonlin- earity in mass-supercritical and energy-subcritical case. Pohozaev identity, we established a threshold condition space. By sharp Hardy-Littlewood-Sobolev inequality and the which leads to a global existence of solutions in energy
基金Supported in part by the National Natural Science Foundation of China under Grant No.11301564
文摘We investigate the nonlinear Schrdinger equation iut＋△u＋｜u｜^p-1u = 0 with 1＋4/N 〈 p 〈 1＋4/（N-2）（when N = 1,2,1 ＋4/N 〈 p 〈 ∞） in energy space H^1 and study the divergent property of infinite-variance and nonradial solutions.If M（u）^（1-sc）/sc E（u） 〈 M（Q）^（1-sc）/scE（Q） and ｜｜u0｜｜0^（1-sc）/sc ｜｜▽u0｜｜2 〉 ｜｜Q｜｜^（1-sc）/sc ｜▽Q｜｜2,then either u（t） blows up in finite forward time or u（t） exists globally for positive time and there exists a time sequence tn→ ＋∞ such that ｜｜ ▽u（tn）｜｜2 →＋∞.Here Q is the ground state solution of —（1 — sc）Q ＋ △Q ＋ ｜Q｜p-1Q = 0.A similar result holds for negative time.This extend the result of the 3D cubic Schrodinger equation obtained by Holmer to the general mass-supercritical and energy-subcritical case.
