Green function of fourth-order differential operator with eigenparameter-dependent boundary and transmission conditions. (English) Zbl 1370.34047
Summary: We investigate a class of fourth-order regular differential operator with transmission conditions at an interior discontinuous point and the eigenparameter appears not only in the differential equation but also in the boundary conditions. We prove that the operator is symmetric, construct basic solutions of differential equation, and give the corresponding Green’s function of the operator is given.
MSC:
| 34B27 | Green’s functions for ordinary differential equations |
| 34L10 | Eigenfunctions, eigenfunction expansions, completeness of eigenfunctions of ordinary differential operators |
| 47E05 | General theory of ordinary differential operators |
| 34B07 | Linear boundary value problems for ordinary differential equations with nonlinear dependence on the spectral parameter |
Keywords:
fourth-order differential operator; eigenparameter-dependent boundary conditions; transmission conditions; eigenvalues; Green functionReferences:
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