带混合色散项的四阶Hartree方程驻波解的存在性与稳定性
Existence and Stability of Standing Wavesfor the Fourth-Order Hartree Equation withMixed Dispersion Terms
DOI:10.12677/PM.2024.148307,PDF,下载: 1浏览: 30科研立项经费支持
作者:颜春阳：西北师范大学数学与统计学院,甘肃 兰州
关键词:波形分解；驻波解；轨道稳定性；Profile Decomposition；Standing Waves；Orbital Stability
摘要:本文主要研究了如下带有混合色散项的四阶 Hartree 方程驻波解的存在性与轨道稳定性iψ t-Δ 2ψ+uΔψ+(|x| -γ*|ψ| 2ψ=0,其中 0 <γ< 4, μ€ℝ, ψ="ψ(t,x)" : ℝ × ℝ d→ℂ 是复值函数。在L 2-次临界情况下,基于波形分解和广义 Gagliardo-Nirenberg 不等式,证明了该方程驻波解的存在性与轨道稳定性。
Abstract:In this paper, we study the existence and orbital stability of standing waves for the fourth-order Hartree equation with mixed dispersion terms iψ t-Δ 2ψ+uΔψ+(|x| -γ*|ψ| 2ψ=0, where 0 <γ< 4, μ€ℝ, ψ="ψ(t,x)" : ℝ × ℝ d→ℂ is the complex-valued wave function. In the L 2-subcritical case, based on the generalized Gagliardo-Nirenberg inequality and the profile decomposition, we prove existence and orbital stability of standing waves for this equation.
文章引用：颜春阳. 带混合色散项的四阶Hartree方程驻波解的存在性与稳定性[J]. 理论数学, 2024, 14(8): 80-92. https://doi.org/10.12677/PM.2024.148307

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