<abstract><p>In this paper, we consider some boundary value problems composed by coupled systems of second-order differential equations with full nonlinearities and general functional boundary conditions verifying some monotone assumptions. The arguments apply the lower and upper solutions method, and defining an adequate auxiliary, homotopic, and truncated problem, it is possible to apply topological degree theory as the tool to prove the existence of solution. In short, it is proved that for the parameter values such that there are lower and upper solutions, then there is also, at least, a solution and this solution is localized in a strip bounded by lower and upper solutions. As far as we know, it is the first paper where Ambrosetti-Prodi differential equations are considered in couple systems with different parameters.</p></abstract>
The aim of this paper is to analyze the axisymmetric unsteady flow of a nonNewtonian incompressible second order fluid in a straight rigid and impermeable tube with circular cross-section of constant radius. To study this problem, we use the one dimensional (1D) nine-directors Cosserat theory approach which reduces the exact three-dimensional equations to a system depending only on time and on a single spatial variable. From this system we obtain the relationship between mean pressure gradient and volume flow rate over a finite section of the tube. Assuming that the pressure gradient rises and falls exponentially with time, the 3D exact solution for unsteady volume flow rate is compared with the corresponding 1D solution obtained by the Cosserat theory using nine directors.
In this work, we present sufficient conditions in order to establish different types of Ulam stabilities for a class of higher order integro-differential equations. In particular, we consider a new kind of stability, the σ-semi-Hyers-Ulam stability, which is in some sense between the Hyers–Ulam and the Hyers–Ulam–Rassias stabilities. These new sufficient conditions result from the application of the Banach Fixed Point Theorem, and by applying a specific generalization of the Bielecki metric.
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