Premium
Asymptotic behavior of a differential operator with discontinuities at two points
Author(s) -
Yang Qiuxia,
Wang Wanyi
Publication year - 2010
Publication title -
mathematical methods in the applied sciences
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.719
H-Index - 65
eISSN - 1099-1476
pISSN - 0170-4214
DOI - 10.1002/mma.1361
Subject(s) - mathematics , eigenfunction , operator (biology) , differential operator , classification of discontinuities , boundary value problem , completeness (order theory) , mathematical analysis , semi elliptic operator , green's function , sturm–liouville theory , function (biology) , eigenvalues and eigenvectors , biochemistry , physics , chemistry , repressor , quantum mechanics , evolutionary biology , biology , transcription factor , gene
In this paper, we study a Sturm–Liouville operator with eigenparameter‐dependent boundary conditions and transmission conditions at two interior points. By establishing a new operator A associated with the problem, we prove that the operator A is self‐adjoint in an appropriate space H , discuss completeness of its eigenfunctions in H , and obtain its Green function. Copyright © 2010 John Wiley & Sons, Ltd.