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On oscillation and nonoscillation properties of Emden-Fowler difference equations

100%

Cecchi M., Došlá Z., Marini M.

Open Mathematics

2009

tom 7

nr 2

322-334

A characterization of oscillation and nonoscillation of the Emden-Fowler difference equation $$ \Delta (a_n \left| {\Delta x_n } \right|^\alpha sgn\Delta x_n ) + b_n \left| {x_{n + 1} } \right|^\beta sgnx_{n + 1} = 0 $$ is given, jointly with some asymptotic properties. The problem of the coexistence of all possible types of nonoscillatory solutions is also considered and a comparison with recent analogous results, stated in the half-linear case, is made.

Unbounded solutions of third order delayed differential equations with damping term

100%

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

2 Cecchi M.

2 Došlá Z.

2 Marini M.

1 Bartušek M.

1 2011

1 2009

Wyniki wyszukiwania

On oscillation and nonoscillation properties of Emden-Fowler difference equations

Unbounded solutions of third order delayed differential equations with damping term