LIN Zhensheng,LONG Qunfei.The blowing -up phenomena of H2(RN)-solution for some kind of quasi -linear Schrdinger equations[J].Journal of Yanbian University,2021,47(01):21-26.
一类拟线性薛定谔方程的H2(RN)- 解的爆破现象
- Title:
- The blowing -up phenomena of H2(RN)-solution for some kind of quasi -linear Schrödinger equations
- 文章编号:
- 1004-4353(2021)01-0021-06
- Keywords:
- quasi -linear Schrö; dinger equation; H2(RN)-solution; finite time; blow up
- 分类号:
- O175.2
- 文献标志码:
- A
- 摘要:
- 为了获得有非正初始能量解的爆破结果,将参数分成3类(① β≤0, θ<0和2<p≤4+4/N; ② β>0, θ<0和2+4/N<p<2·2*; ③ β>0, θ≥0和4+4/N≤p<2·2*)进行讨论,并在不同参数假设下分别给出了一类拟线性薛定谔方程的H2(RN)-解的爆破现象.研究表明,在第②类情形下,当p趋近于2+4/N时,柯西问题的解在时间无穷大时爆破.本文结果扩展了文献[8]的研究结果.
- Abstract:
- In order to obtain a blow up result for the solutions with non -positive initial energy, we discuss them by dividing the parameters into three categories:(1)β≤0, θ<0 and 2<p≤4+4/N;(2)β>0, θ<0 and 2+4/N<p<2·2*;(3)β>0, θ≥0 and 4+4/N≤p<2·2*. And, with varying different parameter assumptions, we separately prove the blowing -up phenomena of H2(RN)-solution for some quasi -linear Schrödinger equations. The results show that for the second case, p approaching to 2+4/N additionally, the solutions of Cauchy problem blow up when the time tends to infinity. The results of this paper extend the results of the literature [8].
参考文献/References:
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备注/Memo
收稿日期: 2020-11-26
作者简介: 林振生(1983—),男,博士,讲师,研究方向为非线性分析及其应用.
基金项目: 国家自然科学基金面上项目(11871152); 福建省教育厅中青年教师教育科研项目(JT180326); 福建工程学院科研启动基金(GY-Z20090); 贵州师范大学博士科研启动项目(GZNU[2018]34)