Related papers: Monotonicity of solutions to second order linear d…
We determine the order of magnitude of the variance of the Fibonacci partition function. The answer is different to the most naive guess. The proof involves a diophantine system and an inhomogeneous linear recurrence.
In this paper we focus on the study of the monotonicity properties of the residual and the past extropy as well as on some characterization problems. We then apply the derived results to analyze further stochastic aspects of order…
Sobolev-type regularity results are proved for solutions to a class of second order elliptic equations with a singular or degenerate weight, under non-homogeneous Neumann conditions. As an application a Pohozaev-type identity for weak…
We offer an alternative and shorter proof to a result by Jan J.Ub{\o}e about monotonicity properties of a one-dimensional function that appeared in the Mathematical Intelligencer in 2015. Our proof is based on reducing the problem to…
In this paper we consider a class of differential equations with state-dependent delays. We show first and second-order differentiability of the solution with respect to parameters in a pointwise sense and also using the C-norm on the…
A linear equation with coefficients in $\mathbb{F}_q$ is common if the number of monochromatic solutions in any two-coloring of $\mathbb{F}_q^n$ is asymptotically (as $n \to \infty$) at least the number expected in a random two-coloring.…
We explore singular second-order boundary value problems with mixed boundary conditions on a general time scale. Using the lower and upper solutions method combined with the Brouwer fixed point theorem we demonstrate the existence of a…
We propose a modified condition of consistency on cubic lattices for some special classes of two-dimensional discrete equations and prove that the discrete nonlinear equations defined by determinants of matrices of orders N > 2 are…
This paper exhibits a very simple formula for a particular solution of a linear ordinary differential equation with constant real coefficients, P(d/dt)x = f, f a function given by a linear combination of polynomials, trigonometrical and…
In this paper, we first investigate the monotonicity and limit problem of the fractional integral functions. By fixed point theorem and these new results of the fractional integral functions, we present that the Riemann-Liouville fractional…
We study monotonicity and 1-dimensional symmetry for positive solutions with algebraic growth of the following elliptic system: \[ \begin{cases} -\Delta u = -u v^2 & \text{in $\R^N$}\\ -\Delta v= -u^2 v & \text{in $\R^N$}, \end{cases} \]…
We demonstrate a strong form of Nevanlinna's Second Main Theorem for solutions to difference equations f(z+1)=R(z, f(z)), with the coefficients of R growing slowly relative to f, and R of degree at least 2 in the second coordinate.
Determinants and symmetric functions of the eigenvalues of matrices characterizing stochastic processes with indepedent increments. Relationships with Fibonacci numbers are derived.
In this paper, we study the linear complementarity problems on extended second order cones. We convert a linear complementarity problem on an extended second order cone into a mixed complementarity problem on the non-negative orthant. We…
Differential inclusions with compact, upper semi-continuous, not necessarily convex right-hand sides in R^n are studied. Under a weakened monotonicity-type condition the existence of solutions is proved.
We investigate the qualitative properties of the weak solutions to the boundary value problems for the hyperbolic fourth-order linear equations with constant coefficients in the plane bounded domain convex with respect to characteristics.…
We present in this paper a detailed note on the computation of Puiseux series solutions of the Riccatti equation associated with a homogeneous linear ordinary differential equation. This paper is a continuation of [1] which was on the…
We give an algorithm for the class of second order unification problems in which second order variables have at most one occurrence.
In this article we present logarithmic methods for solving first order and second order ordinary differential equations. The essence of the method is that we apply the basic properties derivatives and logarithms to reduce the number of…
We consider positive singular solutions (i.e. with a non-removable singularity) of a system of PDEs driven by $p$-Laplacian operators and with the additional presence of a nonlinear first order term. By a careful use of a rather new version…