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 0d →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...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 0d →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。In this paper, we study the existence and orbital stability of standing waves for thefourth-order Hartree equation with mixed dispersion terms iψt-Δ2ψ+uΔψ+(|x|-γ*|ψ|2ψ=0, where 0d →ℂ is the complex-valued wave function. Inthe L2-subcritical case, based on the generalized Gagliardo-Nirenberg inequality andthe profile decomposition, we prove existence and orbital stability of standing wavesfor this equation.展开更多
文摘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 0d →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。In this paper, we study the existence and orbital stability of standing waves for thefourth-order Hartree equation with mixed dispersion terms iψt-Δ2ψ+uΔψ+(|x|-γ*|ψ|2ψ=0, where 0d →ℂ is the complex-valued wave function. Inthe L2-subcritical case, based on the generalized Gagliardo-Nirenberg inequality andthe profile decomposition, we prove existence and orbital stability of standing wavesfor this equation.