Monotone type discrete analogue for the mixed boundary value problem.

MIXED BOUNDARY VALUE PROBLEM FOR A QUARTER-PLANE WITH A ROBIN CONDITION

We consider a mixed boundary value problem for a quarter-plane with a Robin condition on one edge. We have developed two procedures, one based on the advanced theory of dual integral equations and the other, in our opinion simpler technique, relying on conformal mapping. Both of the procedures are of interest, because the former may be easier to adapt to other boundary value problems.

On the discrete boundary value problem for anisotropic equation

In this paper we consider the discrete anisotropic boundary value problem using critical point theory. Thirstily we apply the direct method of the calculus of variations and the mountain pass technique in order to reach the existence of at least one non-trivial solution. Secondly we derive some version of a discrete three critical point theorem which we apply in order to get the existence of at...

Discrete Mixed Petrov-Galerkin Finite Element Method for a Fourth-Order Two-Point Boundary Value Problem

A quadrature-based mixed Petrov-Galerkin finite element method is applied to a fourth-order linear ordinary differential equation. After employing a splitting technique, a cubic spline trial space and a piecewise linear test space are considered in the method. The integrals are then replaced by the Gauss quadrature rule in the formulation itself. Optimal order a priori error estimates are obtai...

Solvability for a discrete fractional mixed type sum-difference equation boundary value problem in a Banach space

Positive solutions for discrete fractional initial value problem

‎‎In this paper‎, ‎the existence and uniqueness of positive solutions for a class of nonlinear initial value problem for a finite fractional difference equation obtained by constructing the upper and lower control functions of nonlinear term without any monotone requirement‎ .‎The solutions of fractional difference equation are the size of tumor in model tumor growth described by the Gompertz f...