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Green function of fourth-order differential operator with eigenparameter-dependent boundary and transmission conditions

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Abstract

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 function of the operator is given.

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Authors and Affiliations

  1. School of Statistics and Mathematics, Inner Mongolia University of Finance and Economics, Hohhot, 010070, China

    Xin-yan Zhang

  2. School of Mathematical Sciences, Inner Mongolia University, Hohhot, 010021, China

    Jiong Sun

Authors
  1. Xin-yan Zhang
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  2. Jiong Sun
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Correspondence to Jiong Sun.

Additional information

Supported by the National Natural Science Foundation of China under Grant No. 11561050, and supported by the Natural Science Foundation of Inner Mongolia under Grant No. 2016BS0103,2014MS0701, and the Science and Technology Plan Projects of Inner Mongolia under Grant No. NJZY16141, NJZY16142, NJZY16143.

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Zhang, Xy., Sun, J. Green function of fourth-order differential operator with eigenparameter-dependent boundary and transmission conditions. Acta Math. Appl. Sin. Engl. Ser. 33, 311–326 (2017). https://doi.org/10.1007/s10255-017-0661-6

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  • DOI: https://doi.org/10.1007/s10255-017-0661-6

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