Homotopy-like perturbation: General results and applications (Q913214)

As the author stresses the aim of the paper is: a) to unify and simplify a number of proofs of known and frequently used perturbation results related to the generation of contraction semigroups or to the cogeneration of resolvent families, and b) to exhibit and clarify the close connection between very different matters such as additive perturbations, singular ``time-change'' perturbations, and certain important aspects of potential theory. In order to achieve that goal, part I of the paper contains two abstract perturbation results, while part II is dedicated to the applications mentioned above.