OSCILLATORY BEHAVIOR OF SOME CLASSES OF DIFFERENCE AND FUNCTIONAL EQUATIONS

Abstract

This thesis deals with quotOSCILLATORY BEHAVIOR OF SOME newlineCLASSES OF DIFFERENCE AND FUNCTIONAL EQUATIONSquot newlinewhich contains seven chapters. newlineChapter 1 is devoted for necessary introduction, motivation, definitions newlineand review of literature. In chapters 2 and 3, we consider the half-linear newlinedifference equations of the form newlineA (an(Ayn)a) + qny:+1 =0, n E IN newlineand A (07/nr) + qny:04 = 0, n E newlineand discuss its oscillatory properties by employing the techniques such as Ric, newlineatti type transformations, comparison theorems respectively. Bounded and newlinemonotone properties, oscillation and asymptotic behavior of the quasilinear newlinedifference equations of the form newlineA (an-LOYn-ir) = qng + rn newlineand A (an(AYn)) + On) AN) qnf (Ynti) 0 newlinewere studied in Chapters 4 and 5 respectively. Some interesting oscillation newlineresults of the volterra summation equations of the form newlinen- newline/in Pn EK(n,a)f(8)1/3),n E /N newline$=0 newlineand the nonlinear functional equations of the form newlineF(y(g(t))) = p(t)y(t) + q(t) f (y(g2 (t))) newlineare obtained in Chapters 6 and 7 respectively. Examples are given throughout newlinethe thesis, wherever necessary, to illustrate the results.