Abstract
In this paper, we consider some third-order operators with transmission conditions. In particular, it is shown that such operators are formally symmetric in the corresponding Hilbert spaces and we introduce the resolvent operators associated with the differential operators. After showing that the eigenvalues of the problems are real and discrete we introduce some ordinary and Frechet derivatives of the eigenvalues with respect to some elements of data.
Highlights
In [8], the nature of the formally symmetric separated, real-coupled, and complex-coupled boundary conditions for the formally symmetric regular third-order differential equation was introduced and some spectral properties were shared
Readers may find the historical background on odd-order formally symmetric boundary value problems in [8]
The results filled some gaps on third-order boundary value problems, there is still a huge amount of work that needs to be done on such problems
Summary
In [8], the nature of the formally symmetric separated, real-coupled, and complex-coupled boundary conditions for the formally symmetric regular third-order differential equation was introduced and some spectral properties were shared. The results filled some gaps on third-order boundary value problems, there is still a huge amount of work that needs to be done on such problems. This includes the imposing separated, real-coupled, complexcoupled transmission conditions to the solutions of these third-order equations and investigating the spectral properties of such problems. We consider the following third-order equation: l(y) = λy, x ∈ [a, c) ∪
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