Differential Equations in Abstract Cones

We extend the method of quasilinearization to differential equations in abstract normal cones. Under some assumptions, corresponding monotone iterations converge to the unique solution of our problem and this convergence is superlinear or semi–superlinea

Multistep methods for nonlinear boundary-value problems with parameters

AbstractMultistep methods combined with iterative ones are applied to find a numerical solution of ordinary differential equations with parameters. This paper deals with the convergence of such methods. There are some estimations of errors too

Delay integro-differential equations of mixed type in Banach spaces

This paper contains sufficient conditions under which there exist extremal solutions of initial value problems for delay integro-differential equations of mixed type in Banach spaces. We use the monotone iterative technique for proving existence results. Some comparison results are also established

Existence of solutions of boundary value problems for differential equations in which deviated arguments depend on the unknown solution

AbstractThis paper concerns differential equations with boundary conditions. Given are sufficient conditions under which such problems with deviated arguments have a unique solution in a corresponding sector. To obtain existence results we apply a monotone iterative method

Multipoint boundary value problems for ODEs. Part II

summary:We apply the method of quasilinearization to multipoint boundary value problems for ordinary differential equations showing that the corresponding monotone iterations converge to the unique solution of our problem and this convergence is quadratic

Boundary value problems for ODEs

summary:We use the method of quasilinearization to boundary value problems of ordinary differential equations showing that the corresponding monotone iterations converge to the unique solution of our problem and this convergence is quadratic

Delay integro-differential equations of mixed type in Banach spaces

This paper contains sufficient conditions under which there exist extremal solutions of initial value problems for delay integro-differential equations of mixed type in Banach spaces. We use the monotone iterative technique for proving existence results. Some comparison results are also established

First order differential equations with a parameter

Employing the method of upper and lower solutions and monotone iterative technique, existence of extremal solutions to differential equations with a parameter is proved