Interval oscillation criteria for second-order quasi-linear nonhomogeneous differential equations with damping

Abstract

By using two inequalities due to Hölder and Hardy, Littlewood and Polya as well as averaging functions, several interval oscillation criteria are established for the second-order quasi-linear differential equation with forced term of the form ( r( t)| y ′( t)| α−1 y ′( t)) ′+ p( t)| y ′( t)| α−1 y ′( t)+ q( t)| y( t)| β−1 y( t)= e( t) that are different from most known ones in the sense that they are based on the information only on a sequence of subintervals of [ t 0,∞), rather than on the whole half-line, where β> α>0. Our results make use of the oscillatory properties of the forcing term and extend a recent result which is obtained by means of a Picone identity.