Steady states are typically obtained by solving for the derivative to be equal to zero. It looks like you only have one parameter t, so differentiate the function, set it zero and solve for the particular value.
Do you have a differential equation form for the function? Also can you point out to us what the δk(t) refers to?
Typically a steady-state solution deals with a situation where you have an implicit differential equation where the changes depend only on the values that just preceded them (but not always).