Degree Type
Dissertation
Date of Award
2003
Degree Name
Doctor of Philosophy
Department
Mathematics
First Advisor
Rajbir S. Dahiya
Abstract
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.
DOI
https://doi.org/10.31274/rtd-180813-11179
Publisher
Digital Repository @ Iowa State University, http://lib.dr.iastate.edu
Copyright Owner
Tuncay Candan
Copyright Date
2003
Language
en
Proquest ID
AAI3105070
File Format
application/pdf
File Size
111 pages
Recommended Citation
Candan, Tuncay, "Oscillation behavior of higher order functional differential equations with distributed deviating arguments " (2003). Retrospective Theses and Dissertations. 1427.
https://lib.dr.iastate.edu/rtd/1427