摘要
本文考虑如下拟线性薛定谔方程:-Δu+(κu)/2△u^(2)=λ|u|^(p-2)u,x∈Ω,这里u∈H(Ω),2<p<2*,κ>0,N≥3且Ω是有界区域.结合变分方法和摄动讨论,作者证明了存在常数κ0>0,使得对任何的κ∈(0,κ0),这类特征值问题有解(λ,u).特别地,如果限制|u|p^(p)=α,作者发现对任何的κ>0,存在α0>0,使得在α<α0时,该特征值问题的解总是存在的.此外,作者采用不同于Morse迭代的方法构造出了常数κ0和α0的精确表达式.
This paper considers a class of quasilinear Schrodinger equations of the form-Δu+(κu)/2△u^(2)=λ|u|^(p-2)u,x∈Ω,where u∈H(Ω),2<p<2*,κ>0,N≥3andΩbounded domain.Combining variational approaches with perturbation arguments,the authors prove that there exists ko>0 such that for any k E(0,ko)this eigenvalue problem admits a solution(λ,u).More interestingly,if the eigenvalue problem is restricted to|u|p=a,the authors observe that for any k>0,there existsαo>0 such that the solution of the eigenvalue problem exists under the situation ofα<αo.Particularly,the authors construct the accurate expressions of ko and ao and,different from the Morse estimate,the authors use another method to show the Lo estimate.
作者
程永宽
沈尧天
CHENG Yongkuan;SHEN Yaotian(School of Mathematics,South China University of Technology,Guangzhou 510640,China)
出处
《数学年刊（A辑）》
CSCD
北大核心
2023年第2期113-120,共8页
Chinese Annals of Mathematics
基金
广东省基础与应用基础研究基金(No.2020A1515010338)的资助.
