arXiv subjects

Ferenc Hartung

Publications and source records attributed to Ferenc Hartung.

3 recordsLinked to original sources

arXiv2026

On existence, uniqueness and numerical approximation of impulsive differential equations with adaptive state-dependent delays using equations with piecewise-constant arguments

In this paper we consider a class of impulsive nonlinear differential equations with adaptive state-dependent delays. We discuss the existence and uniqueness of solutions of the initial value problem using a Picard-Lindel\"of type argument where we define approximate solutions with the help of equations with piecewise-constant arguments (EPCAs). Moreover, we show that the solutions of the associated EPCAs approximate the solutions of the original impulsive DDE with adaptive state-dependent delay uniformly on compact time intervals. The key assumption underlying both results is that the delayed time function is monotone, or piecewise strictly monotone.

math.DS↗

arXiv2023

Hermite-Hadamard type inequalities by using Newton-Cotes quadrature formulas

A convex function $f:[a,b]\to\mathbb{R}$ satisfies the so-called Hermite-Hadamard inequality $$ f\left(\frac{a+b}{2}\right)\leq \frac{1}{b-a}\int_a^{b}f(t)dt\leq \frac{f(a)+f(b)}{2}. $$ Motivated by the above estimates, in this paper we consider approximately monotone and convex functions, and give upper and lower bounds to the numerical integral mean, i.e., to $\frac1{b-a}\mathcal{I}_{n}(f)$, where $\mathcal{I}_{n}(f)$ denotes some of the most popular Newton-Cotes quadrature formulas.

math.GM↗

arXiv2011

On second-order differentiability with respect to parameters for differential equations with state-dependent delays

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 state-space, assuming that the state-dependent time lag function is piecewise strictly monotone.

math.DS↗