## Perturbation method for abstract second-order inverse problems.(English)Zbl 1186.34020

Summary: 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 $$\phi[u(t)]=g(t)$$ 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.

### MSC:

 34A55 Inverse problems involving ordinary differential equations 34G20 Nonlinear differential equations in abstract spaces 47D03 Groups and semigroups of linear operators
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### References:

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