Test for disconjugacy of a differential inclusion of neutral type.
The boundary value problems for ordinary non-linear differential and difference equations of the fourth order
The Dirichlet boundary value problems for strongly singular higher-order nonlinear functional-differential equations
The a priori boundedness principle is proved for the Dirichlet boundary value problems for strongly singular higher-order nonlinear functional-differential equations. Several sufficient conditions of solvability of the Dirichlet problem under consideration are derived from the a priori boundedness principle. The proof of the a priori boundedness principle is based on the Agarwal-Kiguradze type theorems, which guarantee the existence of the Fredholm property for strongly singular higher-order linear...
The existence of solution for boundary value problems for differential equations with deviating arguments and p-Laplacian
We consider a boundary value problem for a differential equation with deviating arguments and p-Laplacian: , x’(t), x’(τ(t))) = 0, t ∈ [0,1]; t ≤ 0; , t ≥ 1. An existence result is obtained with the help of the Leray-Schauder degree theory, with no restriction on the damping forces d/dt grad F(x).
The numerical solution of boundary-value problems for differential equations with state dependent deviating arguments
A numerical method for the solution of a second order boundary value problem for differential equation with state dependent deviating argument is studied. Second-order convergence is established and a theorem about the asymptotic expansion of global discretization error is given. This theorem makes it possible to improve the accuracy of the numerical solution by using Richardson extrapolation which results in a convergent method of order three. This is in contrast to boundary value problems for...
The -Laplacian and connected pairs of functions.
Theory of linear abstract functional differential equations and applications.
Three positive solutions for -Laplacian functional dynamic equations on time scales.
Three-point boundary value problem of retarded functional-differential equation of the second order with parameter
Traveling wave solutions in a class of higher dimensional lattice differential systems with delays and applications
In this paper, we are concerned with the existence of traveling waves in a class of delayed higher dimensional lattice differential systems with competitive interactions. Due to the lack of quasimonotonicity for reaction terms, we use the cross iterative and Schauder's fixed-point theorem to prove the existence of traveling wave solutions. We apply our results to delayed higher-dimensional lattice reaction-diffusion competitive system.
Travelling wave solutions in delayed cellular neural networks with nonlinear output.
Triple positive solutions for the -Laplacian when is a sup-multiplicative-like function.
Triple positive solutions to initial-boundary value problems of nonlinear delay differential equations.
Two modifications of the Leggett-Williams fixed point theorem and their applications.
Two positive solutions for second-order functional and ordinary boundary-value problems.
Two-point boundary value problems for second order functional differential equations.
Two-point functional boundary value problems without growth restrictions