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On a perturbed nonlinear third order differential equation

Michal Greguš (1997)

Archivum Mathematicum

In this paper we will study some asymptotic properties of a nonlinear third order differential equation viewed as a perturbation of a simpler nonlinear equation investigated recently by the authors in [4].

On asymptotic behavior of solutions of n -th order Emden-Fowler differential equations with advanced argument

Roman Koplatadze (2010)

Czechoslovak Mathematical Journal

We study oscillatory properties of solutions of the Emden-Fowler type differential equation u ( n ) ( t ) + p ( t ) | u ( σ ( t ) ) | λ sign u ( σ ( t ) ) = 0 , where 0 < λ < 1 , p L loc ( + ; ) , σ C ( + ; + ) and σ ( t ) t for t + . Sufficient (necessary and sufficient) conditions of new type for oscillation of solutions of the above equation are established. Some results given in this paper generalize the results obtained in the paper by Kiguradze and Stavroulakis (1998).

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