%0 Journal Article %T A class of fourth order differential operators with transmission conditions %J Iranian Journal of Science %I Springer %Z 2731-8095 %A Yang, Q. X %A Wang, W. Y. %D 2011 %\ 12/06/2011 %V 35 %N 4 %P 323-332 %! A class of fourth order differential operators with transmission conditions %K Differential operator %K eigenvalues %K eigenfunctions %K Green function %K completeness %R 10.22099/ijsts.2011.2158 %X We investigate a class of fourth-order differential operators with eigenparameter dependent boundary conditions and transmission conditions. A self-adjoint linear operator A is defined in a suitable Hilbert space H such that the eigenvalues of such a problem coincide with those of A . We discuss asymptotic behavior of its eigenvalues and completeness of its eigenfunctions. Finally, we obtain the representation of its Green function. %U https://ijsts.shirazu.ac.ir/article_2158_424501ad4b2de2356056969b1ec44293.pdf