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Unboundedness results for systems

100%

Lugo G., Palladino F.

Open Mathematics

2009

tom 7

nr 4

741-756

We study k th order systems of two rational difference equations $$ x_n = \frac{{\alpha + \sum\nolimits_{i = 1}^k {\beta _i x_{n - i} + } \sum\nolimits_{i = 1}^k {\gamma _i y_{n - i} } }} {{A + \sum\nolimits_{j = 1}^k {B_j x_{n - j} + } \sum\nolimits_{j = 1}^k {C_j y_{n - j} } }},n \in \mathbb{N}, $$ In particular we assume non-negative parameters and non-negative initial conditions. We develop several approaches which allow us to prove that unbounded solutions exist for certain initial conditions in a range of the parameters.

Unbounded solutions of third order delayed differential equations with damping term

75%

Bartušek M., Cecchi M., Došlá Z., Marini M.

Open Mathematics

2011

tom 9

nr 1

184-195

Globally positive solutions for the third order differential equation with the damping term and delay, $$ x''' + q(t)x'(t) - r(t)f(x(\phi (t))) = 0, $$ are studied in the case where the corresponding second order differential equation $$ y'' + q(t)y = 0 $$ is oscillatory. Necessary and sufficient conditions for all nonoscillatory solutions of (*) to be unbounded are given. Furthermore, oscillation criteria ensuring that any solution is either oscillatory or unbounded together with its first and second derivatives are presented. The comparison of results with those in the case when (**) is nonoscillatory is given, as well.

Ograniczanie wyników

2 Open Mathematics

1 Bartušek M.

1 Cecchi M.

1 Došlá Z.

1 Lugo G.

1 Marini M.

1 Palladino F.

1 2011

1 2009

Wyniki wyszukiwania

Unboundedness results for systems

Unbounded solutions of third order delayed differential equations with damping term