一类拟线性薛定谔方程的H^(2)(R^(N))-解的爆破现象

The blowing-up phenomena of H^(2)(R^(N))-solution for some kind of quasi-linear Schrodinger equations

为了获得有非正初始能量解的爆破结果,将参数分成3类(①β≤0,θ<0和2<p≤4+4 N;②β>0,θ<0和2+4 N<p<2·2;③β>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H^(2)(R^(N))[CD2]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.

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 H 2(R N)-solution for some quasi-linear Schrodinger 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].