Oscillation results for second order Nonliner difference equations

Abstract

quotThis thesis deals with quotquotOscillatory properties of solutions of newlinecertain class of second order nonlinear difference equationsquotquot. It newlinecontains six chapters. Chapter 1 gives necessary introduction newlineand motivation. In Chapters 2 and 3, we have obtained sufficient newlineand necessary conditions for the oscillation of solutions of the newlinefollowing difference equations newlineA(a nAyn ) +4)(n, n N0 newlineand newline+ q n yn7 (n) = en ,ne N newlinerespectively. newlineChapters 4 and 5 deal with the oscillatory properties of newlinesecond order quasilinear difference equations of the forms newlineA(an_i Ayn_i I Ayn_i) + qn f(yn) = 0, nEN newlineA(an_i Ayn- i I u-1 Ayn-1) qn f(yn () = 0, n E N newlineA(an_ilAyn_i newlinea-1 newlineAyn_)+ F(n,yn ) = G(n,yn ,Ayn ), nEN(no), newlinerespectively. newlineFinally, in Chapter 6, we obtain criteria for the oscillation newlineof all / bounded solutions of the neutral type second order newlinedifference equations. newlineExamples are given throughout the thesis, wherever newlinenecessary, to illustrate the results.quot newline newline