We linearize (1.1)-(1.2) about a solution 
of (1.1). Replacing 
by 
, f by f + h, (1.1) reads
Neglecting higher order terms and using that , f solve (1.1) we obtain
Similarly, neglecting higher order terms in (1.2) yields
Thus the operator 
is given by
where 
is the solution of (2.1).
In the application to concrete problems, the bulk of the analytical work consists in determining the adjoint operator 
. While an explicit formula for this operator in the functional analytic framework is easy to derive, this formula is not very useful in practice. Thus we derive 
for specific cases in the next section.
