On the periodic boundary-value problem for systems of second-order nonlinear ordinary differential equations

The periodic boundary value problem for systems of secondorder ordinary nonlinear differential equations is considered. Sufficient conditions for the existence and uniqueness of a solution are established.     

Nonzero solutions to a two-point boundary-value periodic problem for differential equations with maxima

We prove a theorem on the unique existence of a solution to a nonlinear equation with maxima and demonstrate its continuous dependence on the initial function and the parameter of the problem. We also establish conditions for the existence of a nonzero solution to a two-point boundary-value periodic problem in dependence of both linear and nonlinear terms of the equation.     

Unique solvability of a non-linear non-local boundary-value problem for systems of non-linear functional differential equations

General conditions for the unique solvability of a non-linear nonlocal boundary-value problem for systems of non-linear functional differential equations are obtained.     

Periodic boundary-value problem for third-order linear functional differential equations

For a linear functional differential equation of the third order {fx481-01}, we establish the theorems on existence and uniqueness of a solution satisfying the conditions {fx481-02}. Here, ℓ is a linear continuous operator transforming the space C([0, ω]; R) into the space L([0, ω]; R) and q ∈ L([0, ω]; R). The problem of nonnegativity of the solution of the analyzed boundary-value problem is also studied. Published in Ukrains’kyi Matematychnyi Zhurnal, Vol. 60, No. 3, pp. 413–425, March, 2008.     

On a periodic boundary value problem for cyclic feedback type linear functional differential systems

Nonimprovable effective sufficient conditions are established for the unique solvability of the periodic problem

Solvability of boundary-value problems for nonlinear fractional differential equations

We consider the existence of nontrivial solutions of the boundary-value problems for nonlinear fractional differential equations

Solvability of inhomogeneous boundary-value problems for fourth-order differential equations

We consider a Cauchy-type boundary-value problem, a problem with three boundary conditions, and the Dirichlet problem for a general typeless fourth-order differential equation with constant complex coefficients and nonzero right-hand side in a bounded domain Ω ⊂ R ² with smooth boundary. By the method of the Green formula, the theory of extensions of differential operators, and the theory of L-traces (i.e., traces associated with the differential operation L), we establish necessary and sufficient (for elliptic operators) conditions of the solvability of each of these problems in the space H ^m (Ω), m ≥ 4.     

A boundary-value problem for systems of nonlinear partial differential equations

We investigate a boundary-value problem for systems of nonlinear partial differential equations and construct a modifed two-sided method for approximate integration of this problem. We assume that the right-hand side of the system is a continuous function with bounded first partial derivatives in the given domain.Translated from Vychislitel'naya i Prikladnaya Matematika, No. 59, pp. 24–31, 1986.     

Solvability of the Cauchy problem for higher-order linear functional differential equations

We obtain necessary and sufficient conditions for the unique solvability of the Cauchy problem for higher-order linear non-Volterra functional differential equations.     

共振情形下四点泛函边值问题解的存在性

运用Mawhin重合度理论,讨论了一类二阶四点泛函边值问题解的存在性和多解性.分别在非线性项f有界和无界的条件下,获得了此类泛函边值问题解的存在性结果.     

Solvability of boundary value problem at resonance for third-order functional differential equations

This paper is devoted to the study of boundary value problem of third-order functional differential equations. We obtain some existence results for the problem at resonance under the condition that the nonlinear terms is bounded or generally unbounded. In this paper we mainly use the topological degree theory.     

Solvability of general boundary-value problems in a half-space for inhomogeneous differential equations with constant coefficients

We present sufficient conditions for the existence of solutions of general boundary-value problems in a half-space for inhomogeneous differential equations with constant coefficients and arbitrary boundary data in the space of tempered distributions.