Oscillation behavior of higher order functional differential equations with distributed deviating arguments
 Publication Year:
 2003

 Bepress 69

 Bepress 33
 Repository URL:
 https://lib.dr.iastate.edu/rtd/1427
 DOI:
 10.31274/rtd18081311179
 Author(s):
 Publisher(s):
 Tags:
 Mathematics; Applied mathematics
thesis / dissertation description
In this thesis we consider oscillatory and nonoscillatory behavior of functional differential equations and study third and nth 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 wellknown 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 nth order homogeneous neutral differential equation with continuous deviating arguments of the form at&sqbl0; xt+pt xtt &sqbr0;n1 '+dcd qt,xf xst,x dx=0. Chapter four is devoted to nth 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 nth order neutral functional differential equation with constant coefficient of the form &sqbl0; xt+lax t+ah+mbxt+b g&sqbr0;n =pcdx txdx+qc dxt+x dx.