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On the structure of solutions of linear partial differential equation\(\sum\limits_{i + j \leqslant n} {a_{ij} p^i q^j \varphi } = 0\) with two independent variables and constant coefficients

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Abstract

this paper is a continuation of [1]. In this paper, the solutions of the more general linear partial differential equation\(\sum\limits_{i + j \leqslant n} {a_{ij} p^i q^j \varphi } = 0\) with two independent variables and constant coefficients are discussed in detail. The general solution which can be used in the approximation to the conditions of the definite solution of the practical problems is presented. To illustrate the use of the results obtained in this paper, some practical examples in mechanics are given.

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References

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Authors and Affiliations

  1. Harbin Institute of Technology, Harbin

    Gai Bing-zheng

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  1. Gai Bing-zheng
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Communicated by Chien Wei-zang

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Bing-zheng, G. On the structure of solutions of linear partial differential equation\(\sum\limits_{i + j \leqslant n} {a_{ij} p^i q^j \varphi } = 0\) with two independent variables and constant coefficients. Appl Math Mech 6, 447–462 (1985). https://doi.org/10.1007/BF01895382

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  • DOI: https://doi.org/10.1007/BF01895382

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