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| 1 | The Nonlinear Schrdinger Equations with Combined Nonlinearities of Power-Type and Hartree-Type显示文摘The primary goal of this paper is to present a comprehensive study of the nonlinear Schrdinger equations with combined nonlinearities of the power-type and Hartreetype.Under certain structural conditions,the authors are able to provide a complete picture of how the nonlinear Schrdinger equations with combined nonlinearities interact in the given energy space.The method used in the paper is based upon the Morawetz estimates and perturbation principles. | Daoyuan FANG Zheng HAN Jialing DAI | 2011 | Chinese Annals of Mathematics,Series B2011，32，3： | 1 |
| 2 | Hartree型非线性薛定谔方程解的无条件唯一性显示文摘本文主要研究了Hartree型非线性薛定谔方程解在Sobolev空间中的无条件唯一性,在证明无条件唯一性的过程中,运用了负阶Sobolev空间,非齐次Strichartz估计以及解的改善正则性. | 武江雪 韩征 方聪慧 付雪 | 2021 | 杭州师范大学学报(自然科学版)2021，20，5： | 0 |
| 3 | 带Hartree型非线性项双调和薛定谔方程解的整体适定性显示文摘主要研究带Hartree型非线性项的聚焦型双调和Schrödinger方程在质量超临界能量次临界条件下解的整体适定性.运用H2中有界序列的Profile分解得到卷积型Gagliardo-Nirenberg不等式的最佳常数,由此证明双调和Schrödinger方程解的整体适定性. | 王雪雯 郭青 | 2021 | 四川师范大学学报(自然科学版)2021，44，6： | 0 |
| 4 | GLOBAL WELL-POSEDNESS AND BLOW-UP FOR THE HARTREE EQUATION显示文摘For 2 < γ < min{4, n}, we consider the focusing Hartree equation iu_t+ △u +(|x|^(-γ)* |u|~2)u = 0, x ∈ R^n.(0.1)Let M [u] and E [u] denote the mass and energy, respectively, of a solution u, and Q be the ground state of-△ Q + Q =(|x|^(-γ)* |Q|~2)Q. Guo and Wang [Z. Angew. Math.Phy.,2014] established a dichotomy for scattering versus blow-up for the Cauchy problem of(0.1) if M [u]^(1-s_c)E [u]^(s_c)< M [Q]^(1-s_c)E [Q]^(s_c)(s_c=(γ-2)/2). In this paper, we consider the complementary case M [u]^(1-s_c)E [u]^(s_c)≥ M [Q]^(1-s_c)E [Q]^(s_c) and obtain a criteria on blow-up and global existence for the Hartree equation(0.1). | 杨凌燕 李晓光 吴永洪 Louis CACCETTA | 2017 | Acta Mathematica Scientia2017，37，4： | 0 |
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