Oscillations of first-order delay differential equations in a critical state

Abstract

Consider the first-order delay differential equation

in the critical case where

Sufficient condltions are established under which all solutions in spite of the fact that the corrrsponding “limiting” equation

admits a non-oscillatory solution .It should be emphasized that the conditions obtained are unimproveble is some sense. Esitimates for the intervals length between successive zeroes are also obtained.

Keywords:

• Oscillation
• Delay differential equation

^{Part of this work was donw while this author wns visitirig the Departmant of Matheniatics. Boston University and would like to exprees his thankfulness for the excellent hospitality.}

^{Part of this work was donw while this author wns visitirig the Departmant of Matheniatics. Boston University and would like to exprees his thankfulness for the excellent hospitality.}

Notes

^{Part of this work was donw while this author wns visitirig the Departmant of Matheniatics. Boston University and would like to exprees his thankfulness for the excellent hospitality.}

Additional information

Notes on contributors

Y. Domshak