Existence of a ground state and blow-up problem for a nonlinear Schrödinger equation with critical growth
Existence of a ground state and blow-up problem for a nonlinear Schrödinger equation with critical growth
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DOI：
10.57262/die/1356012740
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发表时间：
2011-12
影响因子：
1.4
通讯作者：
Takafumi Akahori;S. Ibrahim;Hiroaki Kikuchi;H. Nawa
中科院分区：
文献类型：
--
作者：
Takafumi Akahori;S. Ibrahim;Hiroaki Kikuchi;H. Nawa
在本文中，我们证明了基态解的存在性的能量临界NLS次临界项扰动时，空间维数dgeq 4 $。然而，在三维，我们表明，当扰动足够小，那么这样的解决方案不存在。对于演化方程，我们证明了能量低于基态能量的径向对称解的有限时间爆破的存在性。
In this paper we show the existence of ground-state solutions for the energy-critical NLS perturbed with subcritical terms when the space dimension $d\geq4$. However in dimension three, we show that when the perturbation is small enough, then such solution does not exist. For the evolution equation, we show the existence of finite time blow up of solutions with radially symmetric data with energy below the one of the ground state.