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Boundary-value problems for some higher-order nonclassical differential equations

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Abstract

The paper consists of two parts. The first part deals with the solvability of new boundary-value problems for the model quasihyperbolic equations (−1)p D t 2p u = Au + f(x, t), where p > 1, for a self-adjoint second-order elliptic operator A. For the problems under study, the existence and uniqueness theorems are proved for regular solutions. In the second part, the results obtained in the first part are somewhat sharpened and generalized.

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Authors and Affiliations

  1. Sobolev Institute of Mathematics, Siberian Branch of the Russian Academy of Sciences, Novosibirsk, Russia

    A. I. Kozhanov

  2. FSAEI of Higher Professional Education, Ammosov Northeast Federal University, Yakutsk, Russia

    N. R. Pinigina

Authors
  1. A. I. Kozhanov
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  2. N. R. Pinigina
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Correspondence to A. I. Kozhanov.

Additional information

Original Russian Text © A. I. Kozhanov, N. R. Pinigina, 2017, published in Matematicheskie Zametki, 2017, Vol. 101, No. 3, pp. 403–412.

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Kozhanov, A.I., Pinigina, N.R. Boundary-value problems for some higher-order nonclassical differential equations. Math Notes 101, 467–474 (2017). https://doi.org/10.1134/S0001434617030087

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  • DOI: https://doi.org/10.1134/S0001434617030087

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