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In the theory of neutron fields some problems arise, which may be described by means of integro-differential equations with initial conditions. The aim of the paper is to state a class of problems covering this physical example and to prove the existence, uniqueness and continuous dependence of their solutions on the given data. A variational approach, presented in a previous author's article, is used to establish the definition of generalized (weak) solutions of the Cauchy problem, which is an extension of the concept of generalized solutions of differential equations.
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