Related papers: Second-Order Self-Adjoint Differential Equations U…

Using the new conformable fractional derivative, which differs from the Riemann-Liouville and Caputo fractional derivatives, we reformulate the second-order conjugate boundary value problem in this new setting. Utilizing the corresponding…

In this paper we construct the main algebraic and differential properties and the weight functions of orthogonal polynomial solutions of bivariate second--order linear partial differential equations, which are admissible potentially…

We use the newly introduced conformable fractional derivative, which is different from the Caputo and Riemann-Liouville fractional derivatives, to reformulate several common boundary value problems, including those with conjugate,…

We consider semiclassical orthogonal polynomials on the unit circle associated with a weight function that satisfy a Pearson-type differential equation involving two polynomials of degree at most three. Structure relations and difference…

In this paper, we analyze a second-order differential equation with a piecewise constant argument and reflection coupled to periodic boundary conditions. Our main contribution is the construction of the related Green's function and a…

We study the Lie point symmetries of a general class of partial differential equations (PDE) of second order. An equation from this class naturally defines a second-order symmetric tensor (metric). In the case the PDE is linear on the first…

We show that the definition of a second order superintegrable system on a (pseudo-)Riemannian manifold gives rise to a conformally invariant notion of superintegrability. Conformal equivalence is the natural extension of the well-known…

We consider a boundary value problem involving conformable derivative of order $\alpha ,$ $1<\alpha <2$ and Dirichlet conditions. To prove the existence of solutions, we apply the method of upper and lower solutions together with Schauder's…

The first-order approach to boundary value problems for second-order elliptic equations in divergence form with transversally independent complex coefficients in the upper half-space rewrites the equation algebraically as a first-order…

Nonlinear second-order ordinary differential equations are common in various fields of science, such as physics, mechanics and biology. Here we provide a new family of integrable second-order ordinary differential equations by considering…

Second order linear non-autonomous differential equations with negative stiffness are considered. Using Chetaev-like (Lyapunov-like) functions, necessary (sufficient) conditions are found for the solutions to be bounded for all initial…

We use some properties of solutions of Riccati equation for establishing boundedness and stability criteria for solutions of second order linear ordinary differential equations. We show that the conditions on coefficients of the equations,…

We deal with the construction of linear connections associated with second order ordinary differential equations with and without first order constraints. We use a novel method allowing glueing of submodule covariant derivatives to produce…

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…

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,…

This paper extends the discriminant associated to second order linear constant coefficient differential equations to general second order linear differential equations. The main result of this paper is that the discriminant of a second…

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.

The question of defining unique, generally applicable constrained second, and higher-order, derivatives is investigated. It is shown that second-order constrained derivatives obtained via two successive constrained differentiations provide…

Using conformal coordinates associated with projective conformal relativity we obtain a conformal Klein-Gordon partial differential equation. As a particular case we present and discuss a conformal `radial' d'Alembert-like equation. As a…

For a second-order linear differential equation with two irregular singular points of rank three, multiple Laplace-type contour integral solutions are considered. An explicit formula in terms of the Stokes multipliers is derived for the…