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The influence of the random perturbations on the fourth-order nonlinear Schrödinger equations, , is investigated in this paper. The local well-posedness in the energy space H 2(? n ) are proved for \(p > \tfrac{{n + 4}}{{n + 2}}\), and p ≤ 2# ? 1 if n ≥ 5. Global existence is also derived for either defocusing or focusing L 2-subcritical nonlinearities.
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$iu_t + \Delta ^2 u + \varepsilon \Delta u + \lambda |u|^{p - 1} u = \dot \xi ,(t,x) \in \mathbb{R}^ + \times \mathbb{R}^n ,n \geqslant 1,\varepsilon \in \{ - 1,0, + 1\} ,$
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在RN(N≥2)中讨论一类具时间依赖系数的半线性Schr(o)dinger方程初值问题的H1-适定性.通过Strichartz估计和解的先验估计,得到了系数零点阶数λ与临界适定指数σ之间的关系,在一定条件下证明了该问题的H1-局部适定性和整体适定性. 相似文献