Related papers: Monotone iterative technique for nonlinear fourth …
This paper presents an iteration method for solving linear particle transport problems in binary stochastic mixtures. It is based on nonlinear projection approach. The method is defined by a hierarchy of equations consisting of the…
We explore singular second-order boundary value problems with mixed boundary conditions on a general time scale. Using the lower and upper solutions method combined with the Brouwer fixed point theorem we demonstrate the existence of a…
We provide of a method to integrate first order non-linear systems of differential equations with variable coefficients. It determines approximate solutions given initial or boundary conditions or even for Sturm-Liouville problems. This…
This paper concerns with a mathematical modelling of biological experiments, and its influence on our lives. Fractional hybrid iterative differential equations are equations that interested in mathematical model of biology. Our technique is…
We investigate the use of piecewise linear systems, whose coefficient matrix is a piecewise constant function of the solution itself. Such systems arise, for example, from the numerical solution of linear complementarity problems and in the…
We are concerned with solvability of nonlinear systems involving a discrete singular $\phi$-Laplacian operator of type \begin{equation*} u \mapsto \Delta\left[\phi(\Delta u(n-1))\right] \qquad (n\in \{1, \dots, T\}), \end{equation*}…
Initially introduced in the framework of quantum control, the so-called "monotonic algorithms" have demonstrated excellent numerical performance when dealing with bilinear optimal control problems. This paper presents a unified formulation…
We study the Stokes--Poisson--Boltzmann equations with Dirichlet and Navier boundary conditions. The system consists of the incompressible Stokes equations coupled with a nonlinear Poisson--Boltzmann equation through electrostatic forcing…
We use a recently found method to characterise all the invertible fourth-order difference equations linear in the extremal values based on the existence of a discrete Lagrangian. We also give some result on the integrability properties of…
By topological arguments, we prove new results on the existence, non-existence, localization and multiplicity of nontrivial solutions of a class of perturbed nonlinear integral equations. These type of integral equations arise, for example,…
Motivated by the study of systems of higher order boundary value problems with functional boundary conditions, we discuss, by topological methods, the solvability of a fairly general class of systems of perturbed Hammerstein integral…
In this paper, we investigate the monotonicity of solutions for a nonlinear equations involving the fractional Laplacian with variable exponent. We first prove different maximum principles involving this operator. Then we employ the direct…
In this paper we presents an algorithm for finding a solution of the linear nonhomogeneous quaternionic-valued differential equations. Moveover, several examples shows the feasibility of our algorithm.
In this paper, we consider the problem of solving a constrained system of nonlinear equations. We propose an algorithm based on a combination of the Newton and conditional gradient methods, and establish its local convergence analysis. Our…
In this paper, we analyze nonlinear differential equations subject to generalized boundary conditions. More specifically, we provide a framework from which we can provide conditions, which are straightforward to check, for the solvability…
A class of fourth--order neutral type difference equations with quasidifferences and deviating arguments is considered. Our approach is based on studying the considered equation as a system of a four--dimensional difference system. The…
This paper investigates numerical methods for solving coupled system of nonlinear elliptic problems. We utilize block monotone iterative methods based on Jacobi and Gauss--Seidel methods to solve difference schemes which approximate the…
New problem is considered that is to find nonlinear differential equations with special solutions. Method is presented to construct nonlinear ordinary differential equations with exact solution. Crucial step to the method is the assumption…
In this paper we study the existence and uniqueness of a solution and propose an iterative method for solving a beam problem which is described by the fully fourth order equation $$u^{(4)}(x)=f(x,u(x),u'(x),u'''(x),u'''(x)), \quad 0 < x <…
We establish the existence of weak solutions of coupled systems of elliptic partial differential equations with quasimonotone nonlinearities in the domain interior and on the boundary. When the nonlinearities satisfy some monotonicity…