Related papers: Numerical method for solving the Dirichlet boundar…
The article considers the Dirichlet problem for a high-order mixed-type equation that splits into factors, each of which is a Lavrentiev-Bitsadze equation with its own excellent coefficient. Sufficient conditions are found for the…
We develop a numerical method for solving a system of nonlinear integral equations involving two integral terms: at the current time t, one integral is taken from 0 to t, and a different integral is taken from t to infinity. We prove the…
In this paper we prove the~existence of two non-trivial weak solutions of Dirichlet boundary value problem for p-Laplacian problem with a~singular part and two disturbances satisfying the~proper assumptions. The~abstract existence result we…
This paper presents a set of complete solutions of a nonconvex variational problem with a double-well potential. Based on the canonical duality-triality theory, the associated nonlinear differential equation with either Dirichlet/Neumann or…
A Neural Network (NN) based numerical method is formulated and implemented for solving Boundary Value Problems (BVPs) and numerical results are presented to validate this method by solving Laplace equation with Dirichlet boundary condition…
Using, as main tool, the convergence theorem for discrete martingales and the mean value property of harmonic functions we solve, a particular case of, Dirichlet problem.
We consider a nonlinear boundary value problem driven by a nonhomogeneous differential operator. The problem exhibits competing nonlinearities with a superlinear (convex) contribution coming from the reaction term and a sublinear (concave)…
This paper deals with the boundary value problems for the singularly perturbed differential-algebraic system of equations. The case of turning points has been studied. The sufficient conditions for existence and uniqueness of the solution…
We study existence and uniqueness of solutions to a class of nonlinear degenerate parabolic equations, in bounded domains. We show that there exists a unique solution which satisfies possibly inhomogeneous Dirichlet boundary conditions. To…
Solutions of boundary value problems for a diffusion equation of fractional and variable order in differential and difference settings are studied. It is shown that the method of energy inequalities is applicable to obtaining a priori…
We consider the numerical solution of the equation - \Delta u - f(u) = g, for the unknown u satisfying Dirichlet conditions in a bounded domain. The nonlinearity f has bounded, continuous derivative. The algorithm uses the finite element…
In this work, the Dirac-type integro di{\S}erential system with one classical boundary condition and another nonlocal integral boundary condition is considered. We obtain the asymptotic formulae for the solutions, eigenvalues and nodal…
A Dirichlet-type problem is studied for an equation of even order with variable coefficients. A criterion for the uniqueness of a solution is given. The solution is built in the form of a Fourier series. When justifying the convergence of…
In this work two-point boundary value problem for one class of second order ordinary differential equations with variable coefficients is solved.
A numerical technique used to solve boundary value problems is modified to find periodic steady-state solutions of nonautonomous dynamical systems. The technique uses a matrix representation of the time derivative obtained through…
We consider the unsteady problem for the general planar Broadwell model with four velocities in a rectangular spatial domain over a finite time interval. We impose a class of non-negative initial and Dirichlet boundary data that are bounded…
We investigate solvability of a continuous Dirichlet boundary value problem together with its classical discretization using a gobal diffeomorphism theorem.
We consider existence of periodic boundary value problems of nonlinear second order ordinary differential equations. Under certain half Lipschitzian type conditions several existence results are obtained. As applications positive periodic…
In this paper we study an inverse boundary value problem for the biharmonic operator with first order perturbation. Our geometric setting is that of a bounded simply connected domain in the Euclidean space of dimension three or higher.…
In this work we give an efficient method involving symbolic manipulation, Picard iteration, and auxiliary variables for approximating solutions of two-point boundary value problems.