On nonoscillatory solutions tending to zero of third-order nonlinear differential equations

Abstract The aim of this paper is to present some results concerning with the asymptotic behavior of solutions of nonlinear differential equations of the third-order with quasiderivatives. In particular, we state the necessary and sufficient conditions ensuring the existence of nonoscillatory solutions tending to zero as t → ∞.

[1]  Wan-Tong Li,et al.  Nonoscillation and Oscillation Theory for Functional Differential Equations , 2004 .

[2]  Jozef Džurina,et al.  Asymptotic properties of trinomial delay differential equations , 2009 .

[3]  Agacik Zafer,et al.  Integral criteria for oscillation of third order nonlinear differential equations , 2009 .

[4]  V. Lakshmikantham,et al.  Oscillation Theory of Differential Equations With Deviating Arguments , 1987 .

[5]  B. Baculíková,et al.  Oscillation of third-order neutral differential equations , 2010, Math. Comput. Model..

[6]  Ravi P. Agarwal,et al.  On the oscillation of certain third order nonlinear functional differential equations , 2008, Appl. Math. Comput..

[7]  Jozef Džurina,et al.  Comparison Theorems for Functional Differential Equations , 1993 .

[8]  Ivan Mojsej,et al.  On bounded nonoscillatory solutions of third-order nonlinear differential equations , 2009 .

[9]  Mauro Marini,et al.  On Some Classes of Continuable Solutions of a Nonlinear Differential Equation , 1995 .

[10]  M. Marini,et al.  An equivalence theorem on properties A, B for third order differential equations , 1997 .

[11]  Ivan Mojsej.  Asymptotic properties of solutions of third-order nonlinear differential equations with deviating argument , 2008 .

[12]  M. Marini,et al.  On nonlinear oscillations for equations associated to disconjugate operators , 1997 .

[13]  C. Tunç.  On some qualitative behaviors of solutions to a kind of third order nonlinear delay differential equations , 2010 .

[14]  Ivan Mojsej,et al.  On solutions of third order nonlinear differential equations , 2006 .

[15]  B. Mihalíková,et al.  Boundedness and oscillation of third order neutral differential equations , 2009 .