| Institution: | 1.Department of Mathematical Sciences,Northern Illinois University,DeKalb,USA;2.Department of Applied Mathematics, Faculty of Electrical Engineering and Computing,University of Zagreb,Zagreb,Croatia |
| Abstract: | We consider a class of the second-order quasilinear differential equations. By deriving relations between certain types of monotonic solutions of the quasilinear equation and corresponding reciprocal half-linear equation on a finite interval (a, b), we obtain criteria for all solutions of the main equation, which do not change sign in (a, b), to be non-monotonic in (a, b). This work is also extended to a perturbed half-linear equation as well as to the half-line \((a,\infty )\). |
