Monotone Iterative Technique for the Periodic Solutions of High-Order Delayed Differential Equations in Abstract Spaces

Monotone iterative technique for causal differential equations with upper and lower solutions in the reversed order

*Correspondence: [email protected] Department of Information Engineering, China University of Geosciences Great Wall College, Baoding, Hebei 071000, P.R. China Abstract In this paper, we use monotone iterative technique in the presence of (coupled) upper and lower solutions in the reversed order to discuss the existence of extremal solutions (quasi-solutions) for causal differential equations wit...

Monotone Iterative Technique for Fractional Evolution Equations in Banach Spaces

We investigate the initial value problem for a class of fractional evolution equations in a Banach space. Under some monotone conditions and noncompactness measure conditions of the nonlinearity, the well-known monotone iterative technique is then extended for fractional evolution equations which provides computable monotone sequences that converge to the extremal solutions in a sector generate...

Mixed Monotone Iterative Technique for Abstract Impulsive Evolution Equations in Banach Spaces

Impulsive differential equations are a basic tool for studying evolution processes of real life phenomena that are subjected to sudden changes at certain instants. In view of multiple applications of the impulsive differential equations, it is necessary to develop the methods for their solvability. Unfortunately, a comparatively small class of impulsive differential equations can be solved anal...

On Periodic Solutions of Abstract Differential Equations

ON THE PERIODIC SOLUTIONS OF A CLASS OF nTH ORDER NONLINEAR DIFFERENTIAL EQUATIONS *

The nth order differential equation x + c (t )x + ƒ( t,x) = e(t),n>3 is considered. Using the Leray-Schauder principle, it is shown that under certain conditions on the functions involved, this equation possesses a periodic solution.