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中文摘要：
研究一类具有转移条件和特征参数相关边界条件的不连续的Sturm-Liouville方程.构造了一个新的算子,并且在新的Hilbert空间中证明了其自伴性.构造了基本解,给出了特征值和特征函数的一些性质,以及渐近估计式,证明了特征函数系的完备性,并且得到了问题的格林函数和预解算子.
英文摘要：
In this paper,a discontinuous Sturm-Liouville equation with eigenparameterdependent boundary conditions and transmission conditions is considered.A new operator associated with the problem is constructed,the self-adjointness of the operator in an appropriate Hilbert space is proved,the fundamental solutions are constructed,some properties of the eigenvalues and corresponding eigenfunctions are investigated,the asymptotic formulas for the eigenvalues and eigenfunctions are given,the completeness of eigenfunctions,Green function and the resolvent operator are also involved.
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