Related papers: Numerical method for solving the Dirichlet boundar…
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,…
We design and analyze an iterative two-grid algorithm for the finite element discretizations of strongly nonlinear elliptic boundary value problems in this paper. We propose an iterative two-grid algorithm, in which a nonlinear problem is…
A large class of initial-boundary value problems of linear evolution partial differential equations formulated on the half-line is analyzed via the unified transform method. In particular, explicit formulae are presented for the generalized…
In this paper we use a natural iteration technique to prove existence of solutions to nonlinear Dirichlet problems. Among the examples included is the prescribed mean curvature equation. The nature of the technique allows applications to…
We study the Dirichlet to Neumann operator of the $\overline{\partial}$-Neumann problem, and the relation between the $\overline{\partial}$-Neumann boundary conditions and the Dirichlet to Neumann operator.
A new method for solving stiff boundary value problems is described and compared to other known approaches using the Troesch's problem as a test example. The method is based on the general idea of alternate approximation of either the…
This article develops a solution for an inverse problem through the generalized method of lines. We consider a Laplace equation on a domain with internal and external boundaries with standard Dirichlet boundary conditions. Also, we specify…
This paper investigates the existence of positive solutions for regular discrete second-order single-variable boundary value problems with mixed boundary conditions, including a nonhomogeneous Dirichlet boundary condition, of the form:…
We study a mixed boundary value problem for the $p$-Laplace equation $\Delta_p u=0$ in an open infinite circular half-cylinder with prescribed Dirichlet boundary data on a part of the boundary and zero Neumann boundary data on the rest.…
A finite difference numerical method is investigated for fractional order diffusion problems in one space dimension. For this, a mathematical model is developed to incorporate homogeneous Dirichlet and Neumann type boundary conditions. The…
We consider boundary value problems of the first and third kind for the diffusionwave equation. By using the method of energy inequalities, we find a priori estimates for the solutions of these boundary value problems.
This article studies a dirichlet boundary value problem for singularly perturbed time delay convection diffusion equation with degenerate coefficient. A priori explicit bounds are established on the solution and its derivatives. For…
We consider an inverse boundary value problem for the biharmonic operator with the first order perturbation in a bounded domain of dimension three or higher. Assuming that the first and the zeroth order perturbations are known in a…
In this paper we study some boundary value problems for a fractional analogue of second order elliptic equation with an involution perturbation in a rectangular domain. Theorems on existence and uniqueness of a solution of the considered…
In this paper we apply a scaling invariance analysis to reduce a class of parabolic moving boundary problems to free boundary problems governed by ordinary differential equations. As well known free boundary problems are always non-linear…
We study the Dirichlet boundary value problem for equations with absorption of the form $-\Delta u+g\circ u=\mu$ in a bounded domain $\Omega\subset R^N$ where $g$ is a continuous odd monotone increasing function. Under some additional…
Adomian decomposition method is used for solving the seventh order boundary value problems. The approximate solutions of the problems are calculated in the form of a rapid convergent series and not at grid points. Two numerical examples…
We present a numerical approximation method for linear diffusion-reaction problems with possibly discontinuous Dirichlet boundary conditions. The solution of such problems can be represented as a linear combination of explicitly known…
In this paper we study nonlinear second-order differential inclusions involving the ordinary vector $p$-Laplacian, a multivalued maximal monotone operator and nonlinear multivalued boundary conditions. Our framework is general and unifying…
We consider the $2m$-th order elliptic boundary value problem $Lu=f(x,u)$ on a bounded smooth domain $\Omega\subset\R^N$ with Dirichlet boundary conditions on $\partial\Omega$. The operator $L$ is a uniformly elliptic linear operator of…