Spectrum and Spectral Singularities of a Quadratic Pencil of a Schr?dinger Operator with Boundary Conditions Dependent on the Eigenparameter  

作　　者：Xiang ZHU Zhao Wen ZHENG Kun LI 

机构地区：[1]School of Mathematical Sciences,Qufu Normal University,Qufu 273165,P.R.China [2]College of Mathematics and Systems Science,Guangdong Polytechnic Normal University,Guangzhou 510665,P.R.China

出　　处：《Acta Mathematica Sinica,English Series》2023年第11期2164-2180,共17页数学学报（英文版）

基　　金：the NSF of Shandong Province(Grant Nos.ZR2023MA023,ZR2020QA009,ZR2020QA010);the NNSF of China(Grant No.61973183);the Youth Creative Team Sci-Tech Program of Shandong Universities(Grant No.2019KJI007)。

摘　　要：In this paper,we consider the following quadratic pencil of Schr?dinger operators L(λ)generated in L~2(R~+)by the equation−y″+[p(x)+2λq(x)]y=λ^(2)y,x∈R^(+)=[0,+∞)with the boundary condition y′(0)/y(0)=β_(1)λ+β0-α_(1)λ+α0,where p(x)and q(x)are complex valued functions andα_(0),α_(1),β_(0),β_(1)are complex numbers withα_(0)β_(1)-α_(1)β_(0)≠0.It is proved that L(λ)has a finite number of eigenvalues and spectral singularities,and each of them is of a finite multiplicity,if the conditions p(x),q′(x)∈AC(R^(+)),limx→∞[|p(x)|+|q(x)|+|q′(x)|]=0 and sup 0≤x<+∞{eε√x[|p′(x)|+|q″(x)|]}<+∞hold,whereε>0.

关 键 词：Schrodinger operator Strum-Liouville problems finite spectrum eigenparameter dependence 

分 类 号：O175[理学—数学]