In this work, we prove the existence of a center manifold for some partial functional differential equations, whose linear part is not necessarily densely defined but satisfies the Hille-Yosida condition. The attractiveness of the center manifold is also shown when the unstable space is reduced to zero. We prove that the flow on the center manifold is completely determined by an ordinary differ...

We study quasilinear systems of parabolic partial differential equations with fully nonlinear boundary conditions on bounded or exterior domains. Our main results concern the asymptotic behavior of the solutions in the vicinity of an equilibrium. The local center, center–stable, and center–unstable manifolds are constructed and their dynamical properties are established using nonautonomous cuto...

The center manifold theorem is a model reduction technique for determining the local asymptotic stability of an equilibrium of a dynamical system when its linear part is not hyperbolic. The overall system is asymptotically stable if and only if the center manifold dynamics is asymptotically stable. This allows for a substantial reduction in the dimension of the system whose asymptotic stability...

In this paper, we introduce a new class of set-valued mappings which is called MD-type mappings. This class of mappings is a set-valued case of a class of the D-type mappings. The class of D-type mappings is a generalization of nonexpansive mappings that recently introduced by Kaewkhao and Sokhuma. The class of MD-type mappings includes upper semi-continuous Suzuki type mappings, upper semi-con...

The Lippmann-Schwinger equation for positronium-proton elastic scattering lacks a first-order term because the center of mass and center of charge are coincident. A consequence of this is that the high-energy behavior of the phase shift is governed by the second-Born approximation. Asymptotic analysis indicates that the high-energy form of the phase shift is dL;O(1/k ), where k is the incident ...

This paper provides new results for the tracking control of a quadrotor unmanned aerial vehicle (UAV). The dynamics of the quadrotor UAV are expressed globally on the configuration manifold of the special Euclidean group, and we construct geometric controllers to track outputs that correspond to each of three flight modes, namely (1) almost global asymptotic tracking of the attitude of the quad...

A call center with both contract and non-contract customers was giving priority to the contract customers only in off-peak hours, precisely when having priority was least important. In this paper we investigate whether this is rational behavior on the part of the call center and what the implications are for customers. In particular, we show that under contracts on the percentile of delay, whic...

here, a predator-prey model with hassell-varley type functional responses is studied. some sufficient conditions are obtained for the permanence and global asymptotic stability of the system by using comparison theorem and constructing a suitable lyapunov functional. moreover, an example is illustrated to verify the results by simulation.