Deflection of elastic ring

Hello Everybody, this is my first post here.

I am currently working on finding the analytical solutions of deformation of thin elastic ring on elastic foundation, with centre fixed. A radial point load is applied at a point. I have derived equations of motion, but i am stuck at boundary conditions. What will be the boundary conditions(BC's) here in rings? In beams, the displacements and moment/force at the ends were specified,(4th order equation and 4 BC's, so the complete solution)  but here its all absorbed in periodicity. Equation of motion came out to be of 6th order, for that i will be needing 6 BC's , I am unable to figure out what they will be.  

Can anyone please help?