Related papers: Weak-Coppel problem for a class of Riccati differe…
We study the set of T-periodic solutions of a class of T-periodically perturbed Differential-Algebraic Equations with separated variables. Under suitable hypotheses, these equations are equivalent to separated variables ODEs on a manifold.…
We present a multi-parameter non-constant-invariant class of Abel ordinary differential equations with the following remarkable features. This one class is shown to unify, that is, contain as particular cases, all the integrable classes…
We associate to an arbitrary $\mathbb Z$-gradation of the Lie algebra of a Lie group a system of Riccati-type first order differential equations. The particular cases under consideration are the ordinary Riccati and the matrix Riccati…
We introduce the notion of Differential Sequences of ordinary differential equations. This is motivated by related studies based on evolution partial differential equations. We discuss the Riccati Sequence in terms of symmetry analysis,…
This paper investigates the existence of weak solutions of biquasilinear boundary value problem for a coupled elliptic-parabolic system of divergence form with discontinuous leading coefficients. The mathematical framework addressed in the…
In this paper we study a system of boundary value problems involving weak p-Laplacian on the Sierpi\'nski gasket in $\mathbb{R}^2$. Parameters $\lambda, \gamma, \alpha, \beta$ are real and $1<q<p<\alpha+\beta.$ Functions $a,b,h :…
We present several new results involving $\Delta(x+U)-\Delta(x)$, where $U = o(x)$ and $$ \Delta(x):=\sum_{n\le x}d(n)-x\log x-(2\gamma-1)x $$ is the error term in the classical Dirichlet divisor problem.
The Riccati equation method is used for study the behavior of solutions of the systems of two linear first order ordinary differential equations. All types of oscillation and regularity of these system are revealed. A generalization of…
This paper is concerned with the study of diagonal Diophantine inequalities of fractional degree $ \theta ,$ where $ \theta >2$ is real and non-integral. For fixed non-zero real numbers $ \lambda_i $ not all of the same sign we write…
Consider real or complex polynomial Riccati differential equations $a(x) \dot y=b_0(x)+b_1(x)y+b_2(x)y^2$ with all the involved functions being polynomials of degree at most $\eta$. We prove that the maximum number of polynomial solutions…
As a first step in exploring time-periodic solutions of the Einstein equations with a negative cosmological constant, we study the cubic conformal wave equation on the Einstein cylinder. Using a combination of numerical and perturbative…
We formulate a conjecture classifying algebraic solutions to (possibly non-linear) algebraic differential equations, in terms of the primes appearing in the denominators of the coefficients of their Taylor expansion at a non-singular point.…
The efficient numerical integration of large-scale matrix differential equations is a topical problem in numerical analysis and of great importance in many applications. Standard numerical methods applied to such problems require an unduly…
We derive an explicit solution to the operator Riccati equation solving the Linear-Quadratic (LQ) optimal control problem for a class of boundary controlled hyperbolic partial differential equations (PDEs). Different descriptions of the…
A system of linear differential equations with oscillatory decreasing coefficients is considered. The coefficients has the form $t^{-\alpha}a(t)$,~$\alpha>0$, where $a(t)$ is trigonometric polynomial with an arbitrary set of frequencies.…
We study the periodic boundary value problem associated with the second order nonlinear differential equation $$ u" + c u' + \left(a^{+}(t) - \mu \, a^{-}(t)\right) g(u) = 0, $$ where $g(u)$ has superlinear growth at zero and at infinity,…
This article is concerned with the existence and multiplicity of positive weak solutions for the following fractional Kirchhoff-Choquard problem: \begin{equation*} \begin{array}{cc} \displaystyle M\left( \|u\|^2\right) (-\Delta)^s u =…
We study the periodic and the Neumann boundary value problems associated with the second order nonlinear differential equation \begin{equation*} u'' + c u' + \lambda a(t) g(u) = 0, \end{equation*} where $g \colon…
Let $d(n)$ be the number of divisors of $n$, let $\gamma$ denote Euler's constant and $$ \Delta(x) := \sum_{n\le x}d(n) - x(\log x + 2\gamma -1) $$ denote the error term in the classical Dirichlet divisor problem, and let $\zeta(s)$ denote…
We improve existing estimates of moments of the Riemann zeta function. As a consequence, we are able to derive new estimates for the asymptotic behaviour of $\sum_{N \alpha \le x} \mathfrak{t}_k(\alpha)$, where $N$ stands for the norm of a…