Open AccessProperties for fourth order discontinuous differential operators with eigenparameter dependent boundary conditions
Author(s) -
Kun Li,
Peng Wang
Publication year - 2022
Publication title -
aims mathematics
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.329
H-Index - 15
ISSN - 2473-6988
DOI - 10.3934/math.2022640
Subject(s) - mathematics , eigenfunction , differential operator , eigenvalues and eigenvectors , boundary value problem , completeness (order theory) , hilbert space , operator (biology) , mathematical analysis , boundary (topology) , green's function , function (biology) , physics , quantum mechanics , chemistry , repressor , evolutionary biology , biology , transcription factor , gene , biochemistry
In this paper, a class of fourth order differential operators with eigenparameter-dependent boundary conditions and transmission conditions is considered. A new operator associated with the problem is established, and the self-adjointness of this operator in an appropriate Hilbert space $ H $ is proved. The fundamental solutions are constructed. Sufficient and necessary conditions of the eigenvalues are investigated. Then asymptotic formulas for the fundamental solutions and the characteristic functions are given. Finally, the completeness of eigenfunctions in $ H $ is given and the Green function is also involved.