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Green’s functions for discrete mTH-order problems*

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Abstract

We investigate an mth-order discrete problem with additional conditions, described by m linearly independent linear functionals. We find the solution to this problem and present a formula and the existence condition of Green’s function if the general solution of a homogeneous equation is known. We obtain a relation between Green’s functions of two nonhomogeneous problems. It allows us to find Green’s function for the same equation, but with different additional conditions. The obtained results are applied to problems with nonlocal boundary conditions.

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Authors and Affiliations

  1. Institute of Mathematics and Informatics, Vilnius University, Akademijos 4, LT-08663, Vilnius, Lithuania

    Artūras Štikonas & Svetlana Roman

Authors
  1. Artūras Štikonas
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  2. Svetlana Roman
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Correspondence to Artūras Štikonas.

Additional information

*This research was funded by a grant (No. MIP-051/2011) from the Research Council of Lithuania.

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Štikonas, A., Roman, S. Green’s functions for discrete mTH-order problems*. Lith Math J 52, 334–351 (2012). https://doi.org/10.1007/s10986-012-9177-1

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  • DOI: https://doi.org/10.1007/s10986-012-9177-1

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