Related papers: Oscillatory criteria for the second order linear o…

We characterize the existence of solutions to the quasilinear Riccati type equation \begin{eqnarray*} \left\{ \begin{array}{rcl} -{\rm div}\,\mathcal{A}(x, \nabla u)&=& |\nabla u|^q + \sigma \quad \text{in} ~\Omega, \\ u&=&0 \quad…

A new, second-order solution in curvilinear coordinates is introduced for the relative motion of two spacecraft on eccentric orbits. The second-order equations for unperturbed orbits are derived in spherical coordinates with true anomaly as…

A new problem is studied, the concept of exactness of a second order nonlinear ordinary differential equations is established. A method is constructed to reduce this class into a first order equations. If the second order equation is not…

Estimates for the spectrum of the Cauchy operator and logarithms of solutions of non-autonomous differential equations in the space, expressed in an arbitrary matrix norm, are found. For equations with periodic coefficients, the lower bound…

Any second order homogeneous linear ordinary differential equation can be transformed into a first order non-linear Riccati equation. We argue that the Riccati form of the linearized fluctuation equations that determine the holographic…

We consider arithmetic three-spheres inequalities to solutions of certain second order quasilinear elliptic differential equations and inequalities with a Riccati-type drift term.

For a second-order elliptic equation of nondivergence form in the plane, we investigate conditions on the coefficients which imply that all strong solutions have first-order derivatives that are Lipschitz continuous or differentiable at a…

Here we give a complete group classification of the general case of linear systems of three second-order ordinary differential equations excluding the case of systems which are studied in the literature. This is given as the initial step in…

In this paper we obtain generalized Calabi-type compactness criteria for complete Riemannian manifolds that allow the presence of negative amounts of Ricci curvature. These, in turn, can be rephrased as new conditions for the positivity,…

A novel formulation of the Lie-Darboux method of obtaining the Riccati equations for the spatial curves in Euclidean three-dimensional space is presented. It leads to two Riccati equations that differ by the sign of torsion. The case of…

We derive a priori estimates for second order derivatives of solutions to a wide calss of fully nonlinear elliptic equations on Riemannian manifolds. The equations we consider naturally appear in geometric problems and other applications…

There is a close connection between stability and oscillation of delay differential equations. For the first-order equation $$ x^{\prime}(t)+c(t)x(\tau(t))=0,~~t\geq 0, $$ where $c$ is locally integrable of any sign, $\tau(t)\leq t$ is…

The linearizability of differential equations was first considered by Lie for scalar second order semi-linear ordinary differential equations. Since then there has been considerable work done on the algebraic classification of linearizable…

The paper concerns the second-order generalized differentiation theory of variational analysis and new applications of this theory to some problems of constrained optimization in finitedimensional spaces. The main attention is paid to the…

We construct an explicit solution of the Cauchy initial value problem for certain diffusion-type equations with variable coefficients on the entire real line. The corresponding Green function (heat kernel) is given in terms of elementary…

We consider divergence-based high order discretizations of an $L^2$-based first order system least squares formulation of a second order elliptic equation with Robin boundary conditions. For smooth geometries, we show optimal convergence…

Some classic second-order sufficient optimality conditions in the calculus of variations are shown to be equivalent, while also introducing a new equivalent second-order condition which is extremely easy to apply: simply integrate a linear…

We prove both necessary and sufficient second order conditions of extrema for variational problems involving any higher order continuously twice differentiable Lagrangians with multi-valued dependent functions of several variables. Our…

An indefinite stochastic Riccati Equation is a matrix-valued, highly nonlinear backward stochastic differential equation together with an algebraic, matrix positive definiteness constraint. We introduce a new approach to solve a class of…

This paper formalize the existence's proof of first-integrals for any second order ODE, allowing to discriminate periodic orbits. Up to the author's knowledge, such a powerful result is not available in the literature providing a tool to…