On differential independence of the Riemann zeta function and the Euler gamma function
On differential operators with integral conditions.
On discontinuous implicit differential equations in ordered Banach spaces with discontinuous implicit boundary conditions
We consider the existence of extremal solutions to second order discontinuous implicit ordinary differential equations with discontinuous implicit boundary conditions in ordered Banach spaces. We also study the dependence of these solutions on the data, and cases when the extremal solutions are obtained as limits of successive approximations. Examples are given to demonstrate the applicability of the method developed in this paper.
On discrete analogues of nonlinear implicit differential equations.
On discreteness of spectrum of a functional differential operator
We study conditions of discreteness of spectrum of the functional-differential operator on . In the absence of the integral term this operator is a one-dimensional Schrödinger operator. In this paper we consider a symmetric operator with real spectrum. Conditions of discreteness are obtained in terms of the first eigenvalue of a truncated operator. We also obtain one simple condition for discreteness of spectrum.
On distance between zeros of solutions of third order differential equations
The lower bounds of the spacings b-a or a’-a of two consecutive zeros or three consecutive zeros of solutions of third order differential equations of the form y”’ + q(t)y’ + p(t)y = 0 (*) are derived under very general assumptions on p and q. These results are then used to show that or as n → ∞ under suitable assumptions on p and q, where ⟨tₙ⟩ is a sequence of zeros of an oscillatory solution of (*). The Opial-type inequalities are used to derive lower bounds of the spacings d-a or b-d for...
On distribution of zeros of solutions of the differential equation
On distributional solutions of some systems of linear differential equations
On effective criteria of solvability of the boundary value problems for ordinary differential equations of the -th order
On efficient method for system of fractional differential equations.
On equation on the line
On equation of finite type, 1-special, with the same central dispersion of the first kind
On equivariant p-harmonic maps
On Euler methods for Caputo fractional differential equations
Numerical methods for fractional differential equations have specific properties with respect to the ones for ordinary differential equations. The paper discusses Euler methods for Caputo differential equation initial value problem. The common properties of the methods are stated and demonstrated by several numerical experiments. Python codes are available to researchers for numerical simulations.
On eventual stability of impulsive systems of differential equations.
On evolution inclusions associated with time dependent convex subdifferentials
On evolution of small spheres in the phase space of a dynamical system*
We study the connection between the entropy of a dynamical system and the boundary distortion rate of regions in the phase space of the system.
On exact controllability of first-order impulsive differential equations.
On exact solutions of a class of interval boundary value problems
In this article, we deal with the Boundary Value Problem (BVP) for linear ordinary differential equations, the coefficients and the boundary values of which are constant intervals. To solve this kind of interval BVP, we implement an approach that differs from commonly used ones. With this approach, the interval BVP is interpreted as a family of classical (real) BVPs. The set (bunch) of solutions of all these real BVPs we define to be the solution of the interval BVP. Therefore, the novelty of the...
On exactness of upper estimates of the characteristic exponent of a linear system with exponentially decreasing perturbations.