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Unbounded solutions of third order delayed differential equations with damping term

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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

1 Open Mathematics

1 Bartušek M.

1 Cecchi M.

1 Došlá Z.

1 Marini M.

1 2011

Wyniki wyszukiwania

Unbounded solutions of third order delayed differential equations with damping term