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Given $k\in\mathbb N$, we define a class of continuous piecewise functions $f$ having abrupt but controlled magnitude changes so that the problem $$\Delta u +f(u)=0,\quad x\in \mathbb R^N, N> 2, $$ has at least $k$ radially symmetric ground…
This paper is devoted to the study of periodic solutions for a radially symmetric semilinear wave equation in an $n$-dimensional ball. By combining the variational methods and saddle point reduction technique, we prove there exist at least…
Complex linear differential equations with entire coefficients are studied in the situation where one of the coefficients is an exponential polynomial and dominates the growth of all the other coefficients. If such an equation has an…
In this paper, we seek to explore under what conditions the periodicity of an entire function $ f(z) $ follows from the periodicity of a differential polynomial in $ f(z) $. We improve and generalize some earlier results and we give other…
Partial differential equations (PDEs) are at the heart of many mathematical and scientific advances. While great progress has been made on the theory of PDEs of standard types during the last eight decades, the analysis of nonlinear PDEs of…
Representations of polynomial covariance commutation relations by pairs of linear integral and differential operators are constructed in the space of infinitely continuously differentiable functions. Representations of polynomial covariance…
Dynamical systems with quadratic or polynomial drift exhibit complex dynamics, yet compared to nonlinear systems in general form, are often easier to analyze, simulate, control, and learn. Results going back over a century have shown that…
We consider the semiconjugate factorization and reduction of order for non-autonomous, nonlinear, higher order difference equations containing linear arguments. These equations have appeared in several mathematical models in biology and…
This work is divided into three parts. The first part concerns polynomials in one variable with all real roots. We consider linear transformations that preserve real rootedness, as well as matrices that preserve interlacing. The second part…
We consider a new class of quaternionic mappings, associated with the spatial partial differential equations. We describe all mappings from this class using four analytic functions of the complex variable.
Differential constraints compatible with the linearized equations of partial differential equations are examined. Recursion operators are obtained by integrating the differential constraints.
Simple form scalar differential equation with delay and non-linear negative periodic feedback is considered. The existence of slowly oscillating periodic solutions with the same period as the feedback coefficient is shown numerically within…
An analysis of a fractional cubic differential equation is presented, which is a generalization of different versions of fractional logistic equations, in order to obtain simpler numerical methods that globalize and extend the results…
Lower and upper bounds for a given function are important in many mathematical and engineering contexts, where they often serve as a base for both analysis and application. In this short paper, we derive piecewise linear and quadratic…
In this paper we present multivariate space-time fractional Poisson processes by considering common random time-changes of a (finite-dimensional) vector of independent classical (non-fractional) Poisson processes. In some cases we also…
In this paper we investigate the properties of the set of T-periodic solutions of semi-explicit parametrized Differential-Algebraic Equations with non-autonomous constraints of a particular type. We provide simple, degree theoretic…
We give a sufficient condition for the surjectivity of partial differential operators with constant coefficients on a class of distributions on R^{n+1} (here we think of there being n space directions and one time direction), that are…
Motivated by Lazer-Leach type results, we study the existence of periodic solutions for systems of functional-differential equations at resonance with an arbitrary even-dimensional kernel and linear deviating terms involving a general delay…
In this paper, we propose a procedure for constructing an infinite number of families of solutions of given linear differential equations with partial derivatives with constant coefficients. We use monogenic functions that are defined on…
We investigate the use of piecewise linear systems, whose coefficient matrix is a piecewise constant function of the solution itself. Such systems arise, for example, from the numerical solution of linear complementarity problems and in the…