Difference method for an elliptic system of nonlinear differential-functional equations.
Difference methods for parabolic functional differential problems of the Neumann type
Nonlinear parabolic functional differential equations with initial boundary conditions of the Neumann type are considered. A general class of difference methods for the problem is constructed. Theorems on the convergence of difference schemes and error estimates of approximate solutions are presented. The proof of the stability of the difference functional problem is based on a comparison technique. Nonlinear estimates of the Perron type with respect to the functional variable for given functions...
Difference methods for the Darboux problem for functional partial differential equations
Distributional derivatives of functions of two variables of finite variation and their application to an impulsive hyperbolic equation
We give characterizations of the distributional derivatives , , of functions of two variables of locally finite variation. Then we use these results to prove the existence theorem for the hyperbolic equation with a nonhomogeneous term containing the distributional derivative determined by an additive function of an interval of finite variation. An application of the above theorem to a hyperbolic equation with an impulse effect is also given.
Dynamics of a two sex population with gestation period
We investigate a mathematical model of population dynamics for a population of two sexes (male and female) in which new individuals are conceived in a process of mating between individuals of opposed sexes and their appearance is postponed by a period of gestation. The model is a system of two partial differential equations with delay which are additionally coupled by mathematically complicated boundary conditions. We show that this model has a global solution. We also analyze stationary ('permanent')...
Eigenvalues and eigenfunctions of the Laplace operator on an equilateral triangle for the discrete case
A discretized boundary value problem for the Laplace equation with the Dirichlet and Neumann boundary conditions on an equilateral triangle with a triangular mesh is transformed into a problem of the same type on a rectangle. Explicit formulae for all eigenvalues and all eigenfunctions are given.
Einige elementare Ungleichungen für Exponentialpolynome.
Exact and approximate solutions of delay differential equations with nonlocal history conditions.
Existence and regularity of local solutions to partial neutral functional-differential equations with infinite delay.
Existence and uniqueness of a classical solution of Fourier's first problem for nonlinear parabolic-elliptic systems.
Existence and uniqueness of solutions Cauchy problem for nonlinear infinite systems of parabolic differential-functional equations.
Existence and Uniqueness of Solutions for Partial Differential-Functional Equations of the First Order with Deviating Argument of the Derivative of Unknown Function
We consider the existence and uniqueness problem for partial differential-functional equations of the first order with the initial condition for which the right-hand side depends on the derivative of unknown function with deviating argument.
Existence and uniqueness of solutions of nonlinear infinite systems of parabolic differential-functional equations
We consider the Fourier first initial-boundary value problem for an infinite system of weakly coupled nonlinear differential-functional equations of parabolic type. The right-hand sides of the system are functionals of unknown functions. The existence and uniqueness of the solution are proved by the Banach fixed point theorem.
Existence and uniqueness of solutions of quasilinear hyperbolic systems of partial differential-functional equations
Existence and uniqueness of solutions to a class of stochastic functional partial differential equations via integral contractors.
Existence of classical solutions for parabolic functional differential equations with initial boundary conditions of Robin type
The paper deals with the initial boundary value problem of Robin type for parabolic functional differential equations. The unknown function is the functional variable in the equation and the partial derivatives appear in the classical sense. A theorem on the existence of a classical solution is proved. Our formulation and results cover differential equations with deviated variables and differential integral problems.
Existence of mild solutions to semilinear evolution inclusions with nonlocal conditions.
Existence of solution of the nonlinear Dirichlet problem for differential-functional equations of elliptic type
Consider a nonlinear differential-functional equation (1) Au + f(x,u(x),u) = 0 where , , G is a bounded domain with (0 < α < 1) boundary, the operator A is strongly uniformly elliptic in G and u is a real function. For the equation (1) we consider the Dirichlet problem with the boundary condition (2) u(x) = h(x) for x∈ ∂G. We use Chaplygin’s method [5] to prove that problem (1), (2) has at least one regular solution in a suitable class of functions. Using the method of upper and lower...
Existence of solutions and monotone iterative method for infinite systems of parabolic differential-functional equations
We consider the Fourier first boundary value problem for an infinite system of weakly coupled nonlinear differential-functional equations. To prove the existence and uniqueness of solution, we apply a monotone iterative method using J. Szarski's results on differential-functional inequalities and a comparison theorem for infinite systems.
Existence of solutions for abstract neutral integro-differential equations with unbounded delay
In this paper we study the existence of classical solutions for a class of abstract neutral integro-differential equation with unbounded delay. A concrete application to partial neutral integro-differential equations is considered.