Related papers: Existence results and iterative method for solving…

By using some elementary techniques from operator theory, we prove constructively prove the existence of solutions to Dirichl\'et problems for planar Jordan domains with at least two boundary curves. An iterative method is thus obtained,…

This paper studies fully discrete finite element approximations to the Navier-Stokes equations using inf-sup stable elements and grad-div stabilization. For the time integration two implicit-explicit second order backward differentiation…

This paper is concerned with boundary integral equation methods for solving the two-dimensional fluid-solid interaction problem. We reduce the problem to three differential systems of boundary integral equations via direct and indirect…

We prove some new results on existence of solutions to first--order ordinary differential equations with deviating arguments. Delay differential equations are included in our general framework, which even allows deviations to depend on the…

In this paper we compute the Leray Schauder degree for a fourth order elliptic boundary value problem with exponential nonlinearity and Navier boundary condition. This will be made by proving a Poincare'-Hopf type theorem. Moreover by using…

We consider an inverse spectral problem with the third-order differential equation and the non-separated boundary conditions. Two theorems on the uniqueness of the solution of this problem are proved, and a method for establishing the…

A new iterative technique is presented for solving of initial value problem for certain classes of multidimensional linear and nonlinear partial differential equations. Proposed iterative scheme does not require any discretization,…

This article investigates the existence and uniqueness of solutions to the second order Volterra integrodifferential equations with nonlocal and boundary conditions through its integral equivalent equations and fixed point of Banach.…

In this paper we consider discrete gradient methods for approximating the solution and preserving a first integral (also called a constant of motion) of autonomous ordinary differential equations. We prove under mild conditions for a large…

In this work, we present a result on the local existence and uniqueness of solutions to nonlinear Partial Differential-Algebraic Equations (PDAEs). By applying established theoretical results, we identify the conditions that guarantee the…

In this paper, we study the biharmonic equation with the Navier boundary conditions in a polygonal domain. In particular, we propose a method that effectively decouples the 4th-order problem into a system of Poisson equations. Different…

In this paper we proved a theorems of existence and uniqueness of solutions of differential equation of second order with fractional derivative in the Kipriyanov sense in lower terms. As a domain of definition of the functions we consider…

In this paper, we consider nonlinearly perturbed Legendre differential equations subject to the usual boundary conditions. For such problems we establish sufficient conditions for the existence of solutions and in some cases we provide a…

A new method is given for proving the global existence of the solution to nonlinear Volterra integral equations. A bound on the solution is derived. The results are based on a nonlinear inequality proved by the author earlier.

This overview is devoted to splitting methods, a class of numerical integrators intended for differential equations that can be subdivided into different problems easier to solve than the original system. Closely connected with this class…

We consider a fourth-order extension of the Allen-Cahn model with mixed-diffusion and Navier boundary conditions. Using variational and bifurcation methods, we prove results on existence, uniqueness, positivity, stability, a priori…

This article is concerned with the existence and uniqueness of solutions to some fractional order boundary value problems. Our results are based on some fixed point theorems. For the applicability of our results, we provide an example.

In this work, we extend the equal-order stabilized scheme discussed in [Franca et al., Comput. Methods Appl. Mech. Engrg. 99 (1992) 209-233] to accommodate slip (i.e., Navier) boundary conditions for the stationary Navier-Stokes equations.…

In this paper we consider a generalized fourth order nonlinear Kirchhoff equation in a bounded domain in $\mathbb R^{N}, N\geq2$ under Navier boundary conditions and with sublinear nonlinearity. We employ a change of variable which reduces…

By means of two fractional order integral inequalities we investigate the existence and uniqueness of the solutions of the fractional nonlinear Volterra integral equation and a fractional nonlinear integrodifferential equation in Banach…