*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 purpose of this paper is concerned with the existence extremal mild solutions for Sobolev type Hilfer fractional evolution equations nonlocal conditions in an ordered Banach spaces E. By using monotone iterative technique coupled method lower and upper solutions, help theory propagation family as well measure noncompactness Sadovskii?s fixed point theorem, we obtain some results equations. ...

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...

Abstract: In this paper, we investigate the existence of solutions for advanced fractional differential equations containing the right-handed Riemann-Liouville fractional derivative both with nonlinear boundary conditions and also with initial conditions given at the end point T of interval [0,T ]. We use both the method of successive approximations, the Banach fixed point theorem and the monot...

A new class of generalized nonlinear variational inclusions involving (A,η)-monotone mappings in the framework of Hilbert spaces is introduced and then based on the generalized resolvent operator technique associated with (A,η)-monotonicity, the approximation solvability of solutions using an iterative algorithm is investigated. Since (A,η)monotonicity generalizes A-monotonicity and H-monotonic...

Abstract This paper is concerned with a class of boundary value problems for the nonlinear impulsive functional integro-differential equations with a parameter by establishing new comparison principles and using the method of upper and lower solutions together with monotone iterative technique. Sufficient conditions are established for the existence of extremal system of solutions for the given...

This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited. We provide a general regularization method for monotone variational inequalities, where the regularizer is a Lipschitz continuous and strongly monotone operator. We also introduce an...

This paper investigates the existence of the extremal solutions to the integral boundary value problem for first-order impulsive functional integrodifferential equations with deviating arguments under the assumption of existing upper and lower solutions in the reversed order. The sufficient conditions for the existence of solutions were obtained by establishing several new comparison principles...

In this paper, by introducing the concept of a generalized concave operator and the properties of cone and monotone iterative technique in ordered Banach spaces, some new existence and uniqueness theorems of fixed points for the operator under more extensive conditions are obtained. Finally, as applications, we apply the results obtained in this paper to study the existence and uniqueness of po...

A new system of nonlinear variational inclusions involving A, η -monotone mappings in the framework of Hilbert space is introduced and then based on the generalized resolvent operator technique associated with A, η -monotonicity, the approximation solvability of solutions using an iterative algorithm is investigated. Since A, η -monotonicity generalizes A-monotonicity and Hmonotonicity, our res...