A variational argument to finding global solutions of a quasilinear Schrodinger equation

作者：Chen Jianqing^*

来源：Communications on Pure and Applied Analysis, 2008, 7(1): 83-88.

• global solutions
• quasilinear Schrodinger equation

We prove a sharp existence result of global solutions of the quasilinear Schrodinger equation
iu(t) + u(xx) + vertical bar u vertical bar(p-2)u + (vertical bar u vertical bar(2))(xx)u = 0, u vertical bar(t=0) = u(0)(x), x is an element of R
for a large class of initial data. The result gives a qualitative description on how small an initial data can ensure the existence of global solutions which sharpen a global existence result with small initial data [ , ].

• 出版日期2008-1
• 单位福建师范大学