Introduction

Abstract

Adjoint equations are increasingly widespread throughout mathematics and its applications. Originally defined by Lagrange, adjoint operators have since been thoroughly substantiated theoretically and broadly applied in solving many problems in mathematical physics. The true meaning of the adjoint equations theory, though, was duly appreciated for the first time by physicists developing quantum mechanics. Schrödinger’s equation required a set of adjoint equations and functions to be developed at least for eigenvalue problems [251]. Adjoint equations became for the first time mathematically indispensable for formulation of the small perturbation theory in spectral problems.