Oscillation behavior of higher order functional differential equations with distributed deviating arguments.

摘要

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 &parl0;bt&parl0;a t&parl0;x′ t&parr0;a&parr0;′ &parr0;′+qt fxt =rt, &parl0;bt&parl0;a t&parl0;x′ t&parr0;a&parr0;′ &parr0;′+qt fxgt =rt , &parl0;bt&parl0;&parl0; atx′ t&parr0;g&parr0;′ &parr0;′+&parl0;q1 txt&parr0; ′+q2t x′t=h t, &parl0;bt&parl0;a tx′t &parr0;′&parr0;′+ i=1>mqit f&parl0;x&parl0;sit &parr0;&parr0;=ht and &parl0;bt&parl0;a tx′t &parr0;′&parr0;′+ c>dqt,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 ′+dc>d 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=1>mpit x&parl0;ti