Related papers: A remark on Pinney's equation

We prove existence and uniqueness of solutions for an entropic version of the semi-geostrophic equations. We also establish convergence to a weak solution of the semi-geostrophic equations as the entropic parameter vanishes. Convergence is…

We give a very simple proof of a strengthened version of Chernoff's Inequality. We derive the same conclusion from much weaker assumptions.

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…

We construct stable periodic solutions for a simple form nonlinear delay differential equation (DDE) with a periodic coefficient. The equation involves one underlying nonlinearity with the multiplicative periodic coefficient. The well-known…

This article deals with the asymptotic behavior of fourth order differential equation where the coefficients are perturbations of linear constant coefficient equation. We introduce a change of variable and deduce that the new variable…

We study the projective systems in both continuous and discrete settings. These systems are linearizable by construction and thus, obviously, integrable. We show that in the continuous case it is possible to eliminate all variables but one…

The mild-slope equation and its various modifications aim to model, with varying degrees of success, linear water wave propagation over sloping or undulating seabed topography. However, despite multiple modifications and attempted…

We use a particular fractional generalization of the ordinary differential equations that we apply to the Riccati equation of constant coefficients. By this means the latter is transformed into a modified Riccati equation with the free term…

We show how to reduce the problem of solving members of a certain family of nonlinear differential equations to that of solving some corresponding linear differential equations.

This paper gives a self-contained, elementary, and largely pictorial statement of Einstein's equation.

A simple method has been introduced to furnish the equilibrium solution of the Wigner equation for all order of the quantum correction. This process builds up a recursion relation involving the coefficients of the different power of the…

We present here the solution of the problem on linearization of fourth-order equations by means of point transformations. We show that all fourth-order equations that are linearizable by point transformations are contained in the class of…

A unified approach to the representation of solutions of linear PDE's with constant coefficients in high dimensions in terms of solutions of the same PDE's in lower dimensions is presented. It is based on the observation that if a function…

A simple solution of Witten's monopole equations is given.

We present the bilinear forms of the (continuous) Painlev\'e equations obtained from the continuous limit of the analogous expresssions for the discrete ones. The advantage of this method is that it leads to very symmetrical results. A new…

We show existence of solutions to the Poisson equation on Riemannian manifolds with positive essential spectrum, assuming a sharp pointwise decay on the source function. In particular we can allow the Ricci curvature to be unbounded from…

The famous result of Landesman and Lazer [10] dealt with resonance at a simple eigenvalue. Soon after publication of [10], Williams [14] gave an extension for repeated eigenvalues. The conditions in Williams [14] are rather restrictive, and…

Two main aims of this paper are to develop a numerical method to solve an inverse source problem for parabolic equations and apply it to solve a nonlinear coefficient inverse problem. The inverse source problem in this paper is the problem…

We investigate the class of regular-ordered word equations. In such equations, each variable occurs at most once in each side and the order of the variables occurring in both sides is the preserved (the variables can be, however, separated…

In in this paper we show how using D.A. it is found a simple change of variables (c.v.) that brings us to obtain differential equations simpler than the original one. In a pedagogical way (at least we try to do that) and in order to make…