Analysis of a non-classically damped engineering structure, which is subjected to an external excitation, leads to the solution of a system of second order ordinary differential equations. Although there exists a large variety of powerful numerical methods to accomplish this task, in some cases it is convenient to formulate the explicit inversion of the respective quadratic fundamental system. The presented contribution uses and extends concepts in matrix polynomial theory and proposes an implementation...

Dans cet article, nous établissons le caractère résurgent-sommable de séries formelles ramifiées solutions d’une classe d’équations différentielles linéaires. Nous analysons d’une part le problème de la dépendance analytique des sommes de Borel de telles séries par rapport aux paramètres de cette classe d’équations différentielles linéaires d’ordre deux, et d’autre part, nous analysons la structure résurgente complète associée à ces séries formelles via l’outil des singularités générales (ou microfonctions)....

The main purpose of this paper is to consider the analytic solutions of the non-homogeneous linear differential equation $f^{\left(k\right)}+a_{k-1}\left(z\right)f^{(k-1)}+\cdots +a₁\left(z\right)f^{\text{'}}+a₀\left(z\right)f=F\left(z\right)$, where all coefficients $a₀,a₁,...,a_{k-1}$, F ≢ 0 are analytic functions in the unit disc = z∈ℂ: |z|<1. We obtain some results classifying the growth of finite iterated order solutions in terms of the coefficients with finite iterated type. The convergence exponents of zeros and fixed points of solutions are also investigated.

This paper is devoted to considering the complex oscillation of differential polynomials generated by meromorphic solutions of the differential equation $$f^{\left(k\right)}+A_{k-1}\left(z\right)f^{(k-1)}+\cdots +A_1\left(z\right)f^{\text{'}}+A_0\left(z\right)f=0,$$ where $A_i\left(z\right)$$(i=0,1...$

This paper is devoted to considering the iterated order and the fixed points of some differential polynomials generated by solutions of the differential equation $$f^{{}^{\text{'}\text{'}}}+A_1\left(z\right)f^{{}^{\text{'}}}+A_0\left(z\right)f=F,$$ where $A_1\left(z\right)$, $A_0\left(z\right)$$(\neg \equiv 0)...$

We investigate the exponent of convergence of the zero-sequence of solutions of the differential equation $f^{\left(k\right)}+a_{k-1}\left(z\right)f^{(k-1)}+\cdots +a₁\left(z\right)f^{\text{'}}+D\left(z\right)f=0$, (1) where $D\left(z\right)=Q₁\left(z\right)e^{P₁\left(z\right)}+Q₂\left(z\right)e^{P₂\left(z\right)}+Q₃\left(z\right)e^{P₃\left(z\right)}$, P₁(z),P₂(z),P₃(z) are polynomials of degree n ≥ 1, Q₁(z),Q₂(z),Q₃(z),$a_j\left(z\right)$ (j=1,..., k-1) are entire functions of order less than n, and k ≥ 2.