Browsing by Subject "differential equation"

Now showing 1 - 6 of 6

Access status: Open Access ,
Comparison of properties of solutions of differential equations and recurrence equations with the same characteristic equation (on example of third order linear equations with constant coefficients)
(2006) Mikołajski, Jarosław; Schmeidel, Ewa
Third order linear homogeneous differential and recurrence equations with constant coefficients are considered. We take the both equations with the same characteristic equation. We show that these equations (differential and recurrence) can have solutions with different properties concerning oscillation and boundedness. Especially the numbers of suitable types of solutions taken out from fundamental sets are presented. We give conditions under which the asymptotic properties considered are the same for the both equations.
Access status: Open Access ,
Forced oscillation and asymptotic behavior of solutions of linear differential equations of second order
(Wydawnictwa AGH, 2022) Shoukaku, Yutaka
The paper deals with the second order nonhomogeneous linear differential equation $(p(t) y'(t))' + q(t) y(t) = f(t),$ which is oscillatory under the assumption that $p(t)$ and $q(t)$ are positive, continuously differentiable and monotone functions on $[0,\infty)$. Throughout this paper we shall use pairs of quadratic forms, which obtained by different methods than Kusano and Yoshida. This form will lead to a property of qualitative behavior, including amplitudes and slopes, of oscillatory solutions of the above equation. In addition, we will discuss the existence of three types (moderately bounded, small, large) of oscillatory solutions, which are based on results due to Kusano and Yoshida.
Access status: Open Access ,
Improved iterative oscillation tests for first-order deviating differential equations
(Wydawnictwa AGH, 2018) Chatzarakis, George E.; Jadlovská, Irena
In this paper, improved oscillation conditions are established for the oscillation of all solutions of differential equations with non-monotone deviating arguments and nonnegative coefficients. They lead to a procedure that checks for oscillations by iteratively computing $\lim \sup$ and $\lim \inf$ on terms recursively defined on the equation's coefficients and deviating argument. This procedure significantly improves all known oscillation criteria. The results and the improvement achieved over the other known conditions are illustrated by two examples, numerically solved in MATLAB.
Access status: Open Access ,
Note on the stability of first order linear differential equations
(2012) Bojor, Florin
In this paper, we will prove the generalized Hyers-Ulam stability of the linear differential equation of the form $y'(x)+f(x)y(x)+g(x)=0$ under some additional conditions.
Access status: Open Access ,
Oscillations of equations caused by several deviating arguments
(Wydawnictwa AGH, 2019) Chatzarakis, George E.
Linear delay or advanced differential equations with variable coefficients and several not necessarily monotone arguments are considered, and some new oscillation criteria are given. More precisely, sufficient conditions, involving $\lim\sup$ and $\lim\inf$, are obtained, which essentially improve several known criteria existing in the literature. Examples illustrating the results are also given, numerically solved in MATLAB.
Access status: Restricted ,
Struktura algebraiczna zbioru generatorów wieloparametrowych grup Liego
(Data obrony: 2010-07-05) Pajda, Anna
Wydział Matematyki Stosowanej