# On asymptotic behavior of solutions of *n*-TH order Emden-Fowler differential equations with advanced argument

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DOI: 10.1007/s10587-010-0051-1

- Cite this article as:
- Koplatadze, R. Czech Math J (2010) 60: 817. doi:10.1007/s10587-010-0051-1

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## Abstract

We study oscillatory properties of solutions of the Emden-Fowler type differential equation where 0 <

$$
u^{(n)} (t) + p(t)|u(\sigma (t))|^\lambda signu(\sigma (t)) = 0,
$$

*λ*< 1,*p*∈*L*_{loc}(ℝ_{+}; ℝ),*σ*∈*C*(ℝ_{+}; ℝ_{+}) and*σ*(*t*) ≥*t*for*t*∈ ℝ_{+}.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).

### Keywords

proper solutionproperty Aproperty B### MSC 2010

34K1534C10## Copyright information

© Mathematical Institute, Academy of Sciences of Czech Republic 2010