This paper deals with the existence of positive solutions for some boundary value problems of the singular differential equations on the whole line. Our approach is based on the fixed point theorem and the monotone iterative technique. Without the assumption of the existence of lower and upper solutions, we obtain not only the existence of nonnegative solutions for the problems, but also establ...

where f : (0, 1) × [0,+∞) → [0,+∞), g : [0, 1]× [0,+∞) → [0,+∞), 0 < ζ < 1, ς > 0, and ςζ < 1, f may be singular at t = 0 and/or t = 1. Under some rather simple conditions, by means of monotone iterative technique, a necessary and sufficient condition for the existence of positive solutions is established, a result on the existence and uniqueness of the positive solution and the iterative seque...

*Correspondence: [email protected] 1College of Science, China Agricultural University, Beijing, 100083, China Full list of author information is available at the end of the article Abstract This paper investigates the existence of concave positive solutions and establishes corresponding iterative schemes for a third-order boundary value problem with Riemann-Stieltjes integral boundary conditions....

In this paper, we obtain the existence of positive solutions and establish two corresponding iterative schemes for the following third order three-point boundary value problem { (φ(u′′))′(t) + q(t)f(u(t)) = 0, 0 ≤ t ≤ 1, u(0) = βu(ξ), u′(1) = 0, φ(u′′(0)) = δφ(u′′(ξ)), where φ : R → R is an increasing homeomorphism and positive homomorphism. The main tool is the monotone iterative technique. An...

In this paper, we deal with a coupled system of nonlinear fractional differential equations, which involve the Riemann-Liouville derivatives of different fractional orders. By using the monotone iterative technique combined with the method of upper and lower solutions, we not only obtain the existence of extremal system of solutions, but also establish iterative sequences for approximating the ...

The cone theory together with Mönch fixed point theorem and a monotone iterative technique is used to investigate the positive solutions for some boundary problems for systems of nonlinear second-order differential equations with multipoint boundary value conditions on infinite intervals in Banach spaces. The conditions for the existence of positive solutions are established. In addition, an ex...

We study the existence of positive solutions for a class of m-point boundary value problems on time scales. Our approach is based on the monotone iterative technique and the cone expansion and compression fixed point theorem of norm type. Without the assumption of the existence of lower and upper solutions, we do not only obtain the existence of positive solutions of the problem, but also estab...

This paper deals with the existence and iteration of positive solutions for the following onedimensional p-Laplacian boundary value problems: φp u′ t ′ a t f t, u t , u′ t 0, t ∈ 0, 1 , subject to some boundary conditions. By making use of monotone iterative technique, not only we obtain the existence of positive solutions for the problems, but also we establish iterative schemes for approximat...

This paper deals with discrete monotone iterative algorithms for solving a nonlinear singularly perturbed parabolic problem. A block monotone domain decomposition algorithm based on a Schwarz alternating method and on a block iterative scheme is constructed. This monotone algorithm solves only linear discrete systems at each time level and converges monotonically to the exact solution of the no...