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Linear Partial Differential Equations with Constant Coefficients: an Elementary Proof of an Existence Theorem

Published online by Cambridge University Press:  21 January 2009

D. H. Parsons
D. H. Parsons
Affiliation:
The University, Reading
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We consider a linear partial differential equation with constant coefficients in one dependent and m independent variables, the right-hand side being zero,

P being a symbolic polynomial in D1, …, Dm. If P can be decomposed into two factors, so that the equation can be written

it is evident that the sum of any solution of

and any solution of

is also a solution of (1).

Type
Research Article
Information
Edinburgh Mathematical Notes , Volume 42 , November 1959 , pp. 3 - 5
Copyright
Copyright © Edinburgh Mathematical Society 1959

References

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