Causal difference equations with upper and lower solutions in the reverse order

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...

The method of lower and upper solutions for fourth order equations with the Navier condition

Existence of Extreme Solutions for Fractional Order Boundary Value Problem Using Upper and Lower Solutions Method in Reverse Order

In this paper, we consider the existence of extreme solutions of the boundary value problem for a fractional order differential equation Dδu = f(t, u), t ∈ [0, T ], 0 < δ < 1, 0 < T < ∞, with a nonlinear boundary conditions g(u(0)) = u(T ). Under a lower solution α and un upper solution β with β ≤ α, we establish existence results of extreme solutions by means of the method of upper and lower s...

Differential Equations and the Method of Upper and Lower Solutions

The purpose of this paper is to give an exposition of the method of upper and lower solutions and its usefulness to the study of periodic solutions to differential equations. Some fundamental topics from analysis, such as continuity, differentiation, integration, and uniform convergence, are assumed to be known by the reader. Concepts behind differential equations, initial value problems, and b...

The Method of Lower and Upper Solutions for Some Fourth-order Equations

In this paper, by combining a new maximum principle of fourth-order equations with the theory of eigenline problems, we develop a monotone method in the presence of lower and upper solutions for some fourth-order ordinary differential equation boundary value problem. Our results indicate there is a relation between the existence of solutions of nonlinear fourth-order equation and the first eige...