Doubt about how to solve the system

Questions
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1

I have this problem and I want to solve this and the conditions are:

when p[r] = 0 we have the radius of the star;

and after this lim r-> \infinity R[r] = 0.

How can I solve this problem?
I mean how can I write a looping for solve the equations inside and outside the star simultaneously.

Open in Wolfram Cloud ↗

tryStarobinsky.nb (22.2 KB)

2

There is a problem with your code. You use the strange symbol r\362, that I had never seen, that typesets almost the same as r^2. What was your intention?

Also, equations are written with ==, not with =.