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,    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iψt-Δ2ψ+uΔψ+(|x|-γ*|ψ|2ψ=0,其中 0<γ< 4, μ€ℝ, ψ =ψ(t,x) : ℝ × ℝd →ℂ 是复值函数。在L2-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 iψt-Δ2ψ+uΔψ+(|x|-γ*|ψ|2ψ=0, where 0<γ< 4, μ€ℝ, ψ =ψ(t,x) : ℝ × ℝd →ℂ is the complex-valued wave function. In the L2-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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