On the strong stability of a nonlinear Volterra integro-differential system.
In this paper, the initial-value problem, the problem of asymptotic time behaviour of its solution and the problem of criticality are studied in the case of linear Boltzmann equation for both finite and infinite media. Space of functions where these problems are solved is chosen in such a vay that the range of physical situations considered may be so wide as possible. As mathematical apparatus the theory of positive bounded operators and of semigroups are applied. Main results are summarized in...
Sufficient conditions which guarantee that certain linear integro-differential equation cannot have a positive solution are established.
The existence of a continuous periodic and almost periodic solutions of the nonlinear integral inclusion is established by means of the generalized Schauder fixed point theorem.
In this paper we examine periodic integrodifferential equations in Banach spaces. When the cone is regular, we prove two existence theorems for the extremal solutions in the order interval determined by an upper and a lower solution. Both theorems use only the order structure of the problem and no compactness condition is assumed. In the last section we ask the cone to be only normal but we impose a compactness condition using the ball measure of noncompactness. We obtain the extremal solutions...