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Potential well method for initial boundary value problem of the generalized double dispersion equations
A variational argument to finding global solutions of a quasilinear Schrödinger equation
| 1. | Department of Mathematics, Fujian Normal University, Fuzhou, 350007 |
$iu_t + u_{x x} + |u|^{p-2}u +(|u|^2)_{x x}u = 0,\quad u|_{t=0}=u_0(x),\quad x\in \mathbb R$
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 [7, 10].
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