In this paper, we study the scattering and blow-up dichotomy result of the radial solution to nonlinear Schrodinger equation （NLS） with the combined termsiut＋△u=-｜u｜^4u＋｜u｜^p-1u,1＋4/3〈p〈5in energy space H^...In this paper, we study the scattering and blow-up dichotomy result of the radial solution to nonlinear Schrodinger equation （NLS） with the combined termsiut＋△u=-｜u｜^4u＋｜u｜^p-1u,1＋4/3〈p〈5in energy space H^1（R^3）. The threshold energy is the energy of the ground state W of the focusing, energy critical NLS, which means that the subcritical perturbation does not affect the determination of threshold, but affects the scattering and blow-up dichotomy result with subcriticM threshold energy. This extends algebraic perturbation in a previous work of Miao, Xu and Zhao [Comm. Math. Phys., 318, 767-808 （2013）] to all mass supercritical, energy subcritical perturbation.展开更多
基金Supported by NSFC(Grant Nos.11171033 and 11231006)
文摘In this paper, we study the scattering and blow-up dichotomy result of the radial solution to nonlinear Schrodinger equation （NLS） with the combined termsiut＋△u=-｜u｜^4u＋｜u｜^p-1u,1＋4/3〈p〈5in energy space H^1（R^3）. The threshold energy is the energy of the ground state W of the focusing, energy critical NLS, which means that the subcritical perturbation does not affect the determination of threshold, but affects the scattering and blow-up dichotomy result with subcriticM threshold energy. This extends algebraic perturbation in a previous work of Miao, Xu and Zhao [Comm. Math. Phys., 318, 767-808 （2013）] to all mass supercritical, energy subcritical perturbation.
