Oscillation behavior of higher order functional differential equations with distributed deviating arguments
In this thesis we consider oscillatory and nonoscillatory behavior of functional differential equations and study third and n-th order functional differential equations qualitatively. Usually a qualitative approach is concerned with the behavior of solutions of a given differential equation and does not seek explicit solutions.;This dissertation is divided into five chapters. The first chapter consists of preliminary material which introduce well-known basic concepts. The second chapter deals with the oscillatory behavior of solutions of third order differential equations and functional differential equations with discrete and continuous delay of the form (bt(a t(x' t)a)' )'+qt fxt =rt, (bt(a t(x' t)a)' )'+qt fxgt =rt , (bt(( atx' t)g)' )'+(q1 txt) '+q2t x't=h t, (bt(a tx't )')'+ i=1mqit f(x(sit ))=ht and (bt(a tx't )')'+ cdqt,x fxst,x dx=0. In chapter three we present sufficient conditions for oscillatory behavior of n-th order homogeneous neutral differential equation with continuous deviating arguments of the form at&sqbl0; xt+pt xtt &sqbr0;n-1 '+dcd qt,xf xst,x dx=0. Chapter four is devoted to n-th order neutral differential equation with forcing term of the form &sqbl0;xt+ i=1mpit x(tit )&sqbr0;n +l1a bq1t,x f1(x(s1 t,x))dx +l2ab q2t,xf 2(x(s2t,x ))dx=ht . Lastly, in chapter five we present sufficient conditions involving the coefficients and arguments only for n-th order neutral functional differential equation with constant coefficient of the form &sqbl0; xt+lax t+ah+mbxt+b g&sqbr0;n =pcdx t-xdx+qc dxt+x dx.