Laplasian[F]+a*d(F)/d(teta)=E*F

I worked with cylindrical coordinates (r,teta,z)

(teta is the angle between the x axis and the r vector (in xy plane))

a,E are constants

I got the constrains: z=0 r=a , so the whole problem is on a simple ring

How can I make the 3D PDE just 1D in teta?

Can I use the Laplasian in cylindrical coordinates, and throw away the d/dr and d/dz?

I hope someone can help me.