Related papers: A remark on Pinney's equation
We study self-adjoint matrix polynomial equations in a single variable and prove existence of self-adjoint solutions under some assumptions on the leading form. Our main result is that any self-adjoint matrix polynomial equation of odd…
The analysis of solutions to algebraic equations is further simplified. A couple of functions and their analytic continuation or root findings are required.
The linearization of complex ordinary differential equations is studied by extending Lie's criteria for linearizability to complex functions of complex variables. It is shown that the linearization of complex ordinary differential equations…
We discuss practical methods for computing the space of solutions to an arbitrary homogeneous linear system of partial differential equations with constant coefficients. These rest on the Fundamental Principle of Ehrenpreis-Palamodov from…
In this short note we prove a result that is an extension of an old Olympiad problem and is a very simple variant of the question of finding an approximation for $k$, where it is a nonzero constant and it satisfies the equation $a^k+b^k=c$,…
We establish the existence of at least one solution to a system of two semilinear coupled Poisson equations with asymptotically linear nonlinearities, without imposing the Ambrosetti-Rabinowitz condition or any of its refinements. The proof…
We extend to several variables an earlier result of ours, according to which an entire function of one variable of sufficiently small exponential type, having all derivatives of even order taking integer values at two points, is a…
A standard Hilbert-space proof of Dirichlet's principle is simplified, using an observation that a certain form of min-problem has unique solution, at a specified point. This solves Dirichlet's problem, after it is recast in the required…
We prove a reducibility result for a linear Klein-Gordon equation with a quasi-periodic driving on a compact interval with Dirichlet boundary conditions. No assumptions are made on the size of the driving, however we require it to be fast…
We present a simple method to obtain the solution of a few orbital problems: the Kepler problem, the modified Kepler problem by the addition of an inverse square potential and linear force.
In this paper we present a two-component generalization of the C-integrable Calogero equation (see [1]). This system is C-integrable as well, and moreover we show that the Calogero equation and its two-component generalization are solvable…
The purpose of this paper is to prove directly, by an elementary method, the Poisson probability law. This proof is offered as an alternative to the more usual derivation from binomial distribution in the limit of small probabilities. The…
Discretizations of differential equations are often studied through their modified equation. This is a differential equation, usually obtained as a power series, with solutions that exactly interpolate the discretization. By comparing the…
Finsler's lemma is a classic mathematical result with applications in control and optimization. When the lemma is applied to parameter-dependent LMIs, as such those that arise from problems of robust stability, the extra variables…
We solve an interpolation problem for computing $\zeta(2n)$ in a rather elementary way, by generalizing the main idea in \cite{SE}.
In this note, we present a simple non-directed graph proof of Sharkovsky's theorem which is different from the one given in [2].
In this paper it is shown that the compact linearization approach, that has been previously proposed only for binary quadratic problems with assignment constraints, can be generalized to arbitrary linear equations with positive coefficients…
The reduction of a large number of scalar integrals to a small set of master integrals via Laporta's algorithm is common practice in multi-loop calculations. It is also a major bottleneck in terms of running time and memory consumption. It…
We establish the existence and symmetry of all minimizers of a constrained variational problem involving the fractional gradient. This problem is closely connected to some fractional kinetic equations.
It is demonstrated that a certain integral equation can be solved using the Painleve equation of third kind. Inversely, a special solution of this Painleve equation can be expressed as the ratio of two infinite series of spheroidal…