Witold Kosmala

On the Difference Equation

We show that the difference equation , where , the parameters , and initial values , are real numbers, can be solved in closed form considerably extending the results in the literature. By using obtained formulae, we investigate asymptotic behavior of well-defined solutions of the equation.

Solutions of the Difference Equation

Our goal in this paper is to investigate the long-term behavior of solutions of the following difference equation: 𝑥𝑛

Oscillation theorems for higher order delay equations

The conditions for oscillation of n th order nonlinear ear delay homogeneous differential equation with nl middle term are given

Long-Term Behavior of Solutions of the Difference Equation

We investigate the long-term behavior of solutions of the following difference equation: 𝑥𝑛

More on oscillation ofnth-order equations

In this paper we prove that a higher-order differential equation with one middle term has every bounded solution oscillatory. Moreover, the behavior of unbounded solutions is given. Two other results dealing with positive solutions are also given.

MORE ON OSCILLATION OF nTH-ORDER EQUATIONS

Abstract In this paper we prove that a higher-order differential equation with one middle term has every bounded solution oscillatory. Moreover, the behavior of unbounded solutions is given. Two other results dealing with positive solutions are also given.

On positive solutions of higher order equations

An oscillation result is given for an nth order equation where the forcing term is any continuous function. Number of properties of the positive solutions are given, provided they exist. Moreover, some conditions which guarantee the nonexistence of positive solutions are also given,