Find right ifelse statement

I have a dataframe df().

Furthermore I have a certain value x.

Now I would like to examine three conditions whether there is a column or not:

1) if df[i] >= x : yes

2) if df[i-1] >= df[i] and df[i] >= x:yes

3) df[i+1] >= df[i] and df[i] >= x: yes

Here, 1) is the basic assumption. Other conditions are to be based on it. I tried to do this with a ifelse()function.

ifelse(df <= x, 
   ifelse(df[i-1] <= df[i] , <column>, <no>), 
   ifelse(df[i+1] <= df[i], <column>, <no>))

But it doesn't work. Do you have any idea how to solve the problem ?

Thanks