Interval oscillation criteria for second order forced nonlinear differential equations with damping. (English) Zbl 1004.34019

Summary: By introducting a new integral averaging technique, several oscillation criteria are established for the nonlinear differential equation \[ (r(t) y'(t))'+ p(t) y'(t)+ g(t) f(y(t))= e(t) \] that are different from most known ones in the sense that they are based on the information only on a sequence of subintervals of \([t_0,\infty)\) rather than on the whole half-line. In particular, several examples that dwell upon the importance of these results are included.


34C10 Oscillation theory, zeros, disconjugacy and comparison theory for ordinary differential equations
34C29 Averaging method for ordinary differential equations