Oscillation and asymptotic behavior of neutral and impulsive differential equations

Abstract

The research reported in this thesis deals with the oscillatory and asymptotic behavior newlineof solutions of some neutral and impulsive differential equations. Here we classify newlinethe solutions of second order nonlinear neutral delay differential equations with newlinepositive and negative coefficients with respect to their asymptotic behavior. Also, newlinewe establish some sufficient conditions for the oscillation of all solutions of second newlineorder nonlinear neutral delay differential equations with positive and negative coefficients. newlineNext, we study the oscillatory behavior of solutions of second order mixed type newlineneutral differential equations. Further we present some sufficient conditions for the newlineoscillation of solutions of third order neutral differential equations with mixed nonlinearities. newlineFinally, we establish a global existence result for the second order nonlinear newlineimpulsive differential equations, and we provide some new oscillation criteria for all newlinesolutions of second order impulsive differential equations with mixed nonlinearities. newlineAll these results are obtained by employing Ricatti type transformation, inequalities newlineand fixed point theorems. newline