# Monotonicity properties of oscillatory solutions of differential equation $(a(t)\vert y^{\prime }\vert ^{p-1}y^{\prime })^{\prime }+f(t,y,y^{\prime })=0$

## Miroslav Bartušek and Chrysi G. Kokologiannaki

Address:

Faculty of Sciences, Masaryk University, Department of Mathematics, Kotlářská 2, 611 37 Brno, Czech Rebuplic

Department of Mathematics, University of Patras, 26500 Patras, Greece

E-mail:

bartusek@math.muni.cz

chrykok@math.upatras.gr

Abstract: We obtain monotonicity results concerning the oscillatory solutions of the differential equation $(a(t)\vert y^{\prime }\vert ^{p-1}y^{\prime })^{\prime }+f(t,y,y^{\prime })=0$. The obtained results generalize the results given by the first author in [1] (1976). We also give some results concerning a special case of the above differential equation.

AMSclassification: primary 34C10; secondary 34C15, 34D05.

Keywords: monotonicity, oscillatory solutions.

DOI: 10.5817/AM2013-3-199