Perturbation theory

Perturbation theory refers to any situation in which a solution to an equation is analyzed by using an existing nearby solution (possibly solving a nearby equation rather than the original equation) as a reference. In many cases the reference solution is trivial (the zero solution). In order for perturbation theory to work, one or more of the following should be true:

• The desired initial data should be close to the reference initial data.
• The desired equation should be close to the reference equation.
• The time interval on which the analysis is performed should be small.

More informally, perturbation theory requires the usage of the $\epsilon$ symbol somewhere in the analysis.

Perturbation theory relies heavily on iteration schemes, bootstrap arguments, and the continuity method.