Related papers: On the well posed solutions for nonlinear second o…
The work deals with establishing the solvability of a system of integro-differential equations in the situation of the double scale anomalous diffusion. Each equation of such system involves the sum of the two negative Laplace operators…
We study the existence of positive solutions on the half-line of a second order ordinary differential equation subject to functional boundary conditions. Our approach relies on a combination between the fixed point index for operators on…
In this paper we present a theory for the existence of multiple nontrivial solutions for a class of perturbed Hammerstein integral equations. Our methodology, rather than to work directly in cones, is to utilize the theory of fixed point…
The paper deals with the following system of nonlinear difference equations \begin{equation*} x_{n+1}=ax_{n}^{2}y_{n}+bx_{n}y_{n}^{2},\ y_{n+1}=cx_{n}^{2}y_{n}+dx_{n}y_{n}^{2},\ n\in \mathbb{N}_{0}, \end{equation*} where the initial values…
Using a modified version of Schauder's fixed point theorem, measures of non-compactness and classical techniques, we provide new general results on the asymptotic behavior and the non-oscillation of second order scalar nonlinear…
This paper aims to investigate the existence and uniqueness of solutions for a sixth order differential equation involving nonlocal and integral boundary conditions. Firstly, we obtain the properties of the relevant Green's functions. The…
This paper deals with the existence of solutions to a class of fourth order nonlinear elliptic equations. The technique used relies on critical points theory. The solutions appeared as critical points of a functional restricted to a…
We study a two-point boundary value problem for a linear differen\-tial-algebraic equation with constant coefficients by using the method of parameterization. The parameter is set as the value of the continuously differentiable component of…
In this paper we use the Riccati equation method with other ones to establish global solvability, stability and oscillation criteria for a class of two dimensional nonlinear systems of ordinary differential equations, which is a…
In this paper, we consider a class of nonlinear fractional differential equations involving Hilfer derivative with boundary conditions. First, we obtain an equivalent integral for the given boundary value problem in weighted space of…
The method of parameter variation for linear differential equations is extended to classes of second order nonlinear differential equations. This allows to reduce the latter to first order differential equations. Known classical equations…
The work deals with the studies of the existence of solutions of an integro-differential equation in the situation of the difference of the standard Laplacian and the bi-Laplacian in the diffusion term. The proof of the existence of…
In this article, we propose an idea to develop some sufficient conditions for the existence and uniqueness of a positive definite common solution to a pair of non-linear matrix equations. To proceed this, we present some interesting common…
We construct fundamental solutions of second-order parabolic systems of divergence form with bounded and measurable leading coefficients and divergence free first-order coefficients in the class of $BMO^{-1}_x$, under the assumption that…
In this article we study optimal control problems for systems that are affine with respect to some of the control variables and nonlinear in relation to the others. We consider finitely many equality and inequality constraints on the…
A class of two-dimensional systems of second-order ordinary differential equations is identified in which a system requires fewer Lie point symmetries than required to solve it. The procedure distinguishes among those which are…
A nonlinear inequality is formulated in the paper. An estimate of the rate of growth/decay of solutions to this inequality is obtained. This inequality is of interest in a study of dynamical systems and nonlinear evolution equations. It can…
The purpose of this article is to study quasi linear parabolic partial differential equations of second order, posed on a bounded network, satisfying a nonlinear and non dynamical Neumann boundary condition at the vertices. We prove the…
Lie symmetries of systems of second-order linear ordinary differential equations with constant coefficients are exhaustively described over both the complex and real fields. The exact lower and upper bounds for the dimensions of the maximal…
We obtain explicit formulas for the solutions of the system of second-order difference equations of the form $x_{n+ 1} = \frac{x_n y_{n-1}}{y_n (a_n + b_n x_n y_{n - 1})}, \quad y_{n+1} = \frac{x_{n - 1} y_n}{x_n (c_n+d_n x_{n-1} y_n)}$,…