Perturbation method for abstract second-order inverse problems - Awawdeh, Fadi (Nonlinear analysis, 2010)
We are concerned with an abstract second-order inverse problem. We restrict ourselves here to abstract inverse problems in which, in order to solve the differential equation for u ( t ) , it is necessary to know the value of some operator or functional ϕ [ u ( t ) ] = g ( t ) as a function of the argument t . A new approach based on the perturbation theory of linear operators is introduced. Among the results obtained we point out sufficient conditions of existence and uniqueness of a solution. As a possible application of the abstract theorems, some applications from elasticity theory are given.