Related papers: Second-order linear differential equations with tw…

In this paper we study the local behavior of a solution to second order elliptic operators with sharp singular coefficients in lower order terms. One of the main results is the bound on the vanishing order of the solution, which is a…

We study the Dubrovin equation of the infinite-dimensional 2D Toda Dubrovin-Frobenius manifold at its irregular singularity. We first revisit the definition of the canonical coordinates, proving that they emerge naturally as generalized…

Since the order of elliptic type model equation (Laplace equation) is two [1], [2], then it is natural the order of composite type model equation must be [3] [4] [5] three. At each point of the domain under consideration these equations…

Solving the linear elasticity and Stokes equations by an optimal domain decomposition method derived algebraically involves the use of non standard interface conditions. The one-level domain decomposition preconditioners are based on the…

This paper provides a new formulation of second order stochastic target problems introduced in [SIAM J. Control Optim. 48 (2009) 2344-2365] by modifying the reference probability so as to allow for different scales. This new ingredient…

We describe some monotone properties of solutions to second order linear difference equations with real constant coefficients. As an application, we give a characterization of the Fibonacci numbers.

All second order scalar differential invariants of symplectic hyperbolic and elliptic Monge-Amp\`ere equations with respect to symplectomorphisms are explicitly computed. In particular, it is shown that the number of independent second…

We show that any second order linear ordinary diffrential equation with constant coefficients (including the damped and undumped harmonic oscillator equation) admits an exact discretization, i.e., there exists a difference equation whose…

This paper concerns a second-order differential equation with indefinite and repulsive singularities. It is the first time to study differential equation containing both indefinite and repulsive singularities simultaneously. A set of…

In this paper, we provide a complete Plancherel-Rotach asymptotic analysis of polynomials that satisfy a second-order difference equation with linear coefficients. According to the signs of the parameters, we classify the difference…

An effective method for generating linear equations of maximal symmetry in their much general normal form is obtained. In the said normal form, the coefficients of the equation are differential functions of the coefficient of the term of…

This article deals with the second order linear differential equations with entire coefficients. We prove some results involving conditions on coefficients so that the order of growth of every non-trivial solution is infinite.

We introduce a ten-parameter ordinary linear differential equation of the second order with four singular points. Three of these are finite and regular whereas the fourth is irregular at infinity. We use the tridiagonal representation…

This paper develops a characterisation of when solutions of forced second order linear differential equations converge to the zero solution of the asymptotically stable and unforced second order equation, or when the solution is bounded,…

A second-order regularity theory is developed for solutions to a class of quasilinear elliptic equations in divergence form, including the $p$-Laplace equation, with merely square-integrable right-hand side. Our results amount to the…

In this paper we study analytic (linear or) nonlinear systems of ordinary differential equations, at an irregular singularity of rank one, under nonresonance conditions. It is shown that the formal asymptotic exponential series solutions…

The presence of second-order smoothness for objective functions of optimization problems can provide valuable information about their stability properties and help us design efficient numerical algorithms for solving these problems. Such…

We investigate geometric aspects of co-equational parametric resurgence, by studying physical problems whose formal asymptotic solutions give rise to Borel transforms lying on an algebraic curve. This perspective allows us to elucidate…

In this paper we consider the resolvent Stokes problem in the case there is a small perturbation of the domain caused by a perturbed boundary. Firstly, we prove that the solution of Stokes problem is continuous due to this small…

We consider the asymptotic behaviour of the second discrete Painlev\'{e} equation in the limit as the independent variable becomes large. Using asymptotic power series, we find solutions that are asymptotically pole-free within some region…