Asymptotic behavior of solutions of certain differential equations and inequalities of second order. (English) Zbl 0581.34050
We study the asymptotic behavior of certain classes of nonoscillatory solutions of second order differential equations and inequalities with deviating argument as well as corresponding ordinary differential equations and difference equations. Necessary and/or sufficient conditions for the existence of so-called extremal and nonextremal nonoscillatory solutions are obtained. Some applications to the case of Thomas-Fermi equation are given.
MSC:
| 34K99 | Functional-differential equations (including equations with delayed, advanced or state-dependent argument) |
| 34C10 | Oscillation theory, zeros, disconjugacy and comparison theory for ordinary differential equations |
| 34C15 | Nonlinear oscillations and coupled oscillators for ordinary differential equations |
| 34A40 | Differential inequalities involving functions of a single real variable |
