*Correspondence: [email protected] 1College of Electronic and Information Engineering, Hebei University, Baoding, 071002, China Full list of author information is available at the end of the article Abstract In this paper, by using the method of quasilinearization to discuss the periodic boundary value problem for a nonlinear singular differential system with ‘maxima’, we obtain monotone iterat...

On the background of a careful analysis of linear DAEs, linearizations of nonlinear index2 systems are considered. Finding appropriate function spaces and their topologies allows to apply the standard Implicit Function Theorem again. Both, solvability statements as well as the local convergence of the Newton-Kantorovich method (quasilinearization) result immediately. In particular, this applies...

Optimal boundary control of semilinear parabolic equations requires efficient solution methods in applications. Solution methods bypass the nonlinearity in different approaches. One approach can be quasilinearization (QL) but its applicability is locally in time. Nonetheless, consecutive applications of it can form a new method which is applicable globally in time. Dividing the control problem ...

In this paper, we propose quasilinearization methods that convert nonlocal fully-nonlinear parabolic systems into the quasilinear systems. The serve as important mathematical tools for modelling subgame perfect equilibrium solutions to time-inconsistent dynamic choice problems, which are motivated by study of behavioral economics. Different types were studied but left behind case and connection...