ABSTRACT
Chapter 22 studies equations with Properties à and B͠. These properties are specific to equations with deviating arguments and do not have analogues for ordinary differential equations. In case of both linear and nonlinear minorants, sufficient conditions are established for the given equation to have Property à or B͠. In addition, definition of the oscillatory equation is given (i.e. when all proper solutions of the equation are oscillatory) and sufficient conditions are established for all solutions of the equation to be oscillatory. For quite general equations, the existence of a proper oscillatory solution is proved. A separate subsection (subsection 22.3.2) is dedicated to the equation of Emden-Fowler type, where sufficient conditions are given for all solutions of the given equation to be oscillatory.
