These are my equations that have to been solved:
and this is my notebook that i'm working in. But i don't know what is wrong with that
You must define eq2, eq3, eq4 before feeding them to NDSolve.
eq2, eq3, eq4
NDSolve
The last initial condition must be written with \[Epsilon][r0] ==, and not with \[Epsilon][r0] =.
\[Epsilon][r0] ==
\[Epsilon][r0] =
Your last equation has a p[r] which perhaps should be p[\[Epsilon][r]].
p[r]
p[\[Epsilon][r]]
I'm so sorry that I attached the wrong notebook. Now it's correct but it doesn't working
You didn't resolve the issue with \[Epsilon][r0] =. Also, the initial condition R'[0] == 0 requires r == 0, but your equations are singular at r == 0.
R'[0] == 0
r == 0