OSCILLATION OF FUNCTIONAL DIFFERENTIAL EQUATIONS

(SAHINER) YILMAZ , Yeter
Ph.D., Mathematics
Supervisor : Assoc.Prof. Agacik ZAFER
Co-supervisor :
June 2000, 120 pages

In this thesis oscillation of functional differential equations is analysed. Our dissertation contains five chapter. The first chapter is essentially introductory in nature. In
Chapter 2, we present necessary and sufficient conditions for oscillation of bounded solutions of neutral functional differential equation z(n)(t) + q(t)f(x(s(t))) = h(t)
where z(t) = x(t) + c(t)x(t(t)). In Chapter 3, Chapter 4 and Chapter 5, we study the oscillation of differential equations of the form (a(t)y(x(t))x(n-1)(t))'+
k(t)x(n-1)(t) + q(t)f(x(s(t))) = 0, (a(t)y(x(t))z'(t))' + k(t)z'(t) + q(t)f(x(s(t))) = 0, and z(n)(t) + p(t)f(z(n-1)(t)) +q(t)|x(s(t))|a sgn[x(s(t))] = 0, respectively. The results
obtained in this thesis concerning the above equations are also compared with that of previously obtained ones.

Keywords : Oscillation, Delay Equation, Neutral Equation, PositiveSolution, Nonlinear, Higher Order, Forcing Term, Damping Term.