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# 1. In this paper we construct the Green function and the solution of the equation

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ROCZNIKI POLSKIEGO TOWARZYSTWA MATEMATYCZNEGO Séria I: P RACE MATEMAT Y CZNE X IX (1976)

ilar

( 2 )

(2)

(

)

D

dD 1

heorem

(9)

V n dD y

## /Iи - Л - [ А и + (а2-{-Ь2) Щ - — [AU + (a2 + b2)U] +

(3)

dD

dK

d n T7

dK

(4)

— 1

### 71 —

1

q = 1 Г = ( ® < - y < ) 2 + (®» + y » )2] 1/2>

i= 1 i= 1

heorem

'(

)

e

У п v J i д У п

Vn -

' (

)

(5)

w h e r e

X г

У п „ J __

emma

— 1

E n- 1

owt

E n - 1

(6)

emma

(7)

w h e r e

п- 1

(8)

у

### * < <x>, 0 < y{ < -к (i = 1. ..., n — 3), 0 < <pn_2 < 27c, |J |

= V * ~ 2 V>{ <P l, < P n - b ) l w e g e t

OO О

C 3 { X ) = M æ n

### J

r n - 2 ( r 2 + 0 " w /2 ^ < Ж я п j

RI2 Rl2

Г 7T Z 1

n С[ХД|2(Х')]

### |/( Y ') |d Y '< 2a?n Jf,

/ l / ( V ) | d r ' , E n - l

emma

q

q

(9)

w h e r e

o(q

2

\

v+2

1

Yn J

Ern _ 1

СО Г

3

2

2

Yn

q

2

3

3

~ n+1

e .

2

1

2

01

00 I*

Yn J ,

(10)

0

0

л? /*

У п

J2

1

У п

q

x

q

0

1

2

2 01

У п т т У

У п

1

-<5i 2 1

\J\

2

1

2

2

1

2

2 1

0

1 /2

(11)

'0

2

4

2

) - v~ 1

2

2

2

~ 2v~ 2

2

2

2

2

7 n

j

2 2

2

2

Yn

2

2

### n— 1

5 — Roczniki PTM — Prace Matematyczne XIX

(12)

2

heorem

References

### problem, Comm. Math. 16 (1972), p. 1-35.

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