当前位置: X-MOL 学术Asymptot. Anal. › 论文详情
Our official English website, www.x-mol.net, welcomes your feedback! (Note: you will need to create a separate account there.)
Low and high energy solutions of oscillatory non-autonomous Schrödinger equations with magnetic field
Asymptotic Analysis ( IF 1.4 ) Pub Date : 2020-06-25 , DOI: 10.3233/asy-201629
Youpei Zhang 1, 2 , Xianhua Tang 1
Affiliation  

We are concerned with the mathematical and asymptotic analysis of solutions to the following nonlinear problem −ΔAu=λβ(x)|u|qu+f(|u|)uin Ω,u=0on ∂Ω, where ΔAu is the magnetic Laplace operator, Ω⊂RN is a smooth bounded domain, A:Ω↦RN is the magnetic potential, u:Ω↦C, λ is a real parameter, β∈L∞(Ω,R) is an indefinite potential, q is nonnegative, and f:[0,+∞)↦R is a reaction that oscillates either in a neighborhood of the origin or at infinity. We analyze two distinct cases, in close relationship with the oscillatory growth of the reaction. Additionally, we give asymptotic estimates for the norm of the solutions in related function spaces.

中文翻译:

具有磁场的振荡非自治Schrödinger方程的高能和低能解

我们关注以下非线性问题的解的数学和渐近分析-ΔAu=λβ(x)| u | qu + f(| u |)uinΩ,u = 0 onΩΩ,其中ΔAu是磁性拉普拉斯算子,Ω⊂RN是一个光滑有界域,A:Ω↦RN是磁势,u:Ω↦C,λ是一个实参,β∈L∞(Ω,R)是一个不确定的电位,q是非负的, f:[0,+∞)↦R是在原点附近或无限远处振荡的反应。我们分析了两种不同的情况,与反应的振荡增长密切相关。此外,我们给出了相关函数空间中解范数的渐近估计。
更新日期:2020-06-30
down
wechat
bug