On a decomposition formulae for the solutions of a class of partial pifferential equations of even order

Year 1973, Volume: 22 , 0 - 0, 01.01.1973

S. Süray

https://doi.org/10.1501/Commua1_0000000630

Abstract

A Weinstein and L. E. Payne had obtained decomposition formulae for the Solutions of the equation
T^ k™ u = O,
where
Lk
n S
i=l
32
a xı2
32
+ + —
y
8
In this paper, we will extend the decomposition formulae for the Solutions of the equation
m
a2
i=ı SXj2
V
i-1 Xi d Xj
u = 0.
u
+
d
1. Let us consider the differential operatör
a2 5 ax .2 + -«k (1 Xk a X,■k
k < n)
where e R is an arbitrary constant. Let the function u
u (x
2,.- - ■ ,) e be the solution of the eguation
‘n,
Li
'“k
u = 0.
X
n
a
Such a solution will be denoted by u {aı^}.

Keywords

decomposition formulae, solutions of a class, partial pifferential equations

References

• Ankara Üniversitesi – Communications Faculty of Sciences University of Ankara Series A1 Mathematics and Statistics Dergisi