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

We consider weighted p-Laplace type equations with homogeneous Neumann boundary conditions in convex domains, where the weight is a log-concave function which may degenerate at the boundary. In the case of bounded domains, we provide sharp…

We prove that the curved Ovsienko--Redou operators and a related family of differential operators are formally self-adjoint. This verifies two conjectures of Case, Lin, and Yuan.

Distinguished selfadjoint extensions of operators which are not semibounded can be deduced from the positivity of the Schur Complement (as a quadratic form). In practical applications this amounts to proving a Hardy-like inequality.…

We derive the Lagrangians of the higher-order Painlev\'e equations using Jacobi's last multiplier technique. Some of these higher-order differential equations display certain remarkable properties like passing the Painlev\'e test and…

We show that the theory of self-adjoint differential equations can be used to provide a satisfactory solution of the inverse variational problem in classical mechanics. A Newtonian equation when transformed to the self-adjoint form allows…

This paper concerns local gradient estimates to solutions of general conformally invariant fully nonlinear elliptic equations of second order.

This paper deals with a Tikhonov regularized second-order plus first-order primal-dual dynamical system with time scaling for separable convex optimization problems with linear equality constraints. This system consists of two second-order…

This paper studies formulations of second-order elliptic partial differential equations in nondivergence form on convex domains as equivalent variational problems. The first formulation is that of Smears \& S\"uli [SIAM J.\ Numer.\ Anal.\…

It is classical that univariate algebraic functions satisfy linear differential equations with polynomial coefficients. Linear recurrences follow for the coefficients of their power series expansions. We show that the linear differential…

We consider boundary value problems for stochastic differential equations of second order with a small parameter. For this case we prove a special existence and unicity theorem for strong solutions. The asymptotic behavior of these…

This work is devoted to find the numerical solutions of several one dimensional second-order ordinary differential equations. In a heuristic way, in such equations the quadratic logistic maps regarded as a local function are inserted within…

For a nonlinear ordinary differential equation with time delay, the differentiation of the solution with respect to the delay is investigated. Special emphasis is laid on the second-order derivative. The results are applied to an associated…

In this paper we present a direct formula for the solution of the general second order linear ordinary differential equation as our main result such that the parameters required for the formula are determined using another differential…

In this paper we consider the linear second order partial differential equation with non-constant coefficients; then by using the double convolution product we produce new equations with polynomials coefficients and we classify the new…

In this paper, the author derives an $O(h^4)$-superconvergence for the piecewise linear Ritz-Galerkin finite element approximations for the second order elliptic equation $-\nabla \cdot(A\nabla u)= f$ equipped with Dirichlet boundary…

We study 2D discrete integrable equations of order 1 with respect to one independent variable and $m$ with respect to another one. A generalization of the multidimensional consistency property is proposed for this type of equations. The…

In this paper, we propose a second-order continuous primal-dual dynamical system with time-dependent positive damping terms for a separable convex optimization problem with linear equality constraints. By the Lyapunov function approach, we…

In this paper we implement the Darboux transformation, as well as an analogue of Crum's theorem, for a discrete version of Schr\"odinger equation. The technique is based on the use of first order operators intertwining two difference…

In this note we survey results in recent research papers on the use of Lie groups in the study of partial differential equations. The focus will be on parabolic equations, and we will show how the problems at hand have solutions that seem…

Recently, a new fractional derivative called the conformable fractional derivative is given which is based on the basic limit definition of the derivative in [1]. Then, the fractional versions of chain rules, exponential functions,…