Related papers: A remark on Pinney's equation

The exact solution of a Cauchy problem related to a linear second-order difference equation with constant noncommutative coefficients is reported.

In this paper we consider a generalized Kirchhoff? equation in a bounded domain under the effect of a sublinear nonlinearity. Under suitable assumptions on the data of the problem we show that, with a simple change of variable, the equation…

In this article, we give a formula for the generalization of the binomial coefficient to the complex numbers as a linear combination of $\sinc$ functions. We then give a general formula to compute the integral on the real line of the…

We give a simple proof of a recently result concerning Hardy $q$-inequalities.

We develop a method to recognize admissibility of $\Pi_{2}$-rules, relating this problem to a specific instance of the unification problem with linear constants restriction, called here "unification with simple variable restriction". It is…

In this note, we use the method of [3] to give a simple proof of famous Witten conjecture. Combining the coefficients derived in our note and this method, we can derive more recursion formulas of Hodge integrals.

We find an explicit form of entropy solutions to a Riemann problem for a degenerate nonlinear parabolic equation with piecewise constant velocity and diffusion coefficients. It is demonstrated that this solution corresponds to the minimum…

In this study, a recursive solution technique in conjunction with generalized integrating factors is presented and applied to address first and second order linear differential equations. This approach demonstrates practical utility in…

We present a general formula for the particular solution of an inhomogeneous linear difference equation with variable coefficients. The answer is expressed as a weighted sum of fundamental solutions of the associated linear difference…

We prove an explicit Chinese Remainder Theorem for one variable polynomials with complex coefficients, and derive some consequences.

The work considers the damped Pinney equation, defined as the model arising when a linear in velocity damping term is included in the Pinney equation. In the general case the resulting equation does not admit Lie point symmetries or is…

We present a restricted variable generalization of Warning's Second Theorem (a result giving a lower bound on the number of solutions of a low degree polynomial system over a finite field, assuming one solution exists). This is analogous to…

A recurrence equation is a discrete integrable equation whose solutions are all periodic and the period is fixed. We show that infinitely many recurrence equations can be derived from the information about invariant varieties of periodic…

Bianchi and Don\`{a} [1] have recently reported a proof to the variance formula of von Neumann entropy, which was conjectured in [2] and firstly proved in [3]. The purpose of this short note is to show that, despite having a different…

We will prove the Brannan conjecture for particular values of the parameter. The basic tool of the study is an integral representation published in a recent work [3].

We improve constants in the Rademacher-Menchov inequality.

We exactly solve the (2+1)-dimensional Dirac equation in a constant magnetic field in the presence of a minimal length. Using a proper ansatz for the wave function, we transform the Dirac Hamiltonian into two 2-dimensional non-relativistic…

In this short note, we improve the famous Reid Inequality related to linear operators.

We study general semilinear scalar-field equations on the real line with variable coefficients in the linear terms. These coefficients are uniformly small, but slowly decaying, perturbations of a constant-coefficient operator. We are…

As a first step towards a theory of differential equations involving para-Grassmann variables the linear equations with constant coefficients are discussed and solutions for equations of low order are given explicitly. A connection to…