Oscillation Behavior For A Class Of Nonlinear Functional Differential Equations

Oscillation theory for functional differential equations is an important branch of the qual itative theory of differential equations, it is widely used in control engineering, mechanical v ibration, mechanics and economics. Recently, many research works have been made conc erning the oscillation theory and applications of differential equations.In this thesis, we mainly study oscillatory criteria and asymptotic behavior of third-order differential equationsIn the third chapter, Applying the comparison method we present new criteria for oscill ation or certain asymptotic behavior of non-oscillatory solutions of this equations as ?=0, a=0,b=1.In the fourth chapter, a class of third-order quasi-linear differential equations with conti nuously distributed delay are studied. Applying the generalized Riccati transformation, integr al averaging technique of Philos-type and $Young's\, Inequality$, etc, we present new criter ia for oscillation or certain asymptotic behavior of nonoscillatory solutions of this equations.The result obtained essentially improve and complement earlier ones.