This paper deals with application of the maximum principle for differential equations to the finite difference method for determining upper and lower approximate solutions of the non-linear Burgers’ equation and their error range. In term of mathematical architecture, the paper is based on the maximum principle for parabolic differential equations to establish monotonic residual relations of th...

Abstract In the paper, nonlinear systems of mixed-type functional differential equations are analyzed and existence semi-global global solutions is proved. proofs, monotone iterative technique Schauder-Tychonov fixed-point theorem used. addition to proving solutions, estimates their co-ordinates derived as well. Linear variants results considered illustrated by selected examples.

We consider Initial-Boundary value problems associated with nonlinear hyperbolic partial differential equation in three independent variables, in a general setting wherein the forcing function is a sum of two monotonic functions. Employing natural lower-upper and coupled lower-upper solutions, we develop iterative schemes which converge uniformly and monotonically to the minimal-maximal and cou...

We study the global existence and the global nonexistence of a non-Newtonian polytropic filtration system coupled via nonlinear boundary flux. We first establish a weak comparison principle, then discuss the large time behavior of solutions by using modified upper and lower solution methods and constructing various upper and lower solutions. Necessary and sufficient conditions on the global exi...

This paper focuses on the boundary layer phenomenon arising in the study of singularly perturbed differential equations. Our tools include the method of lower and upper solutions combined with analysis of the integral equation associated with the class of nonlinear equations under consideration. Key words and phrases: singularly perturbed systems, three–point boundary value problem, method of l...

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...