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

Faculty of Sciences, Masaryk University, Department of Mathematics, Kotlářská 2, 611 37 Brno, Czech Rebuplic
Department of Mathematics, University of Patras, 26500 Patras, Greece


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