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Abstract In this thesis, we discuss the oscillatory behavior of solutions of the second -#111;-#114;-#100;-#101;-#114; neutral delay differential equation of the form br r m br (r(t)z’(t)) + q .(t)f (x(o- .(t))). , t ?to, br J =1 br -#119;-#104;-#101;-#114;-#101; br l br i n . br z(t) = x(t) + E p i(t)x(r i(0), 0 5_ p i(t) 5 J . po -lt; co, ,., br i =1 br (t) dt = co . br We introduce new sufficient conditions for oscillation of solutions of the following second -#111;-#114;-#100;-#101;-#114; nonlinear neutral differential equations: br r , -,\ br ( k br r (t) po(t)x(t)+ E p i(t)x(t — t i) br i =1 br k br + E q .(t)f . (x(t — to)) = 0, t J =1 br and br n br r (t)(130(t)x(t)+ pi(t)x(o-(o) I q. (t) f (x(i- . (t))) = 0, t t„. br i=1 \ 1 k br j =1 br Further, we discuss the oscillatory behavior of the second -#111;-#114;-#100;-#101;-#114; quasilinear neutral delay differential equations br (r(t)41 (x(t))I z’(t)la 1 zr(t)) + q (t) f (x (t))) = 0, t -gt; t0 br i =1 br -#119;-#104;-#101;-#114;-#101;and the second -#111;-#114;-#100;-#101;-#114; nonlinear neutral differential equations with deviating arguments of the form: br (r(t)lz”(tr 0)1 ± f j (t ,x(c (t)))=0, t t br J =1 br -#119;-#104;-#101;-#114;-#101; br z(t) = x(t) + E p i(t)x( (t)) and a ? O. br i=1 br Moreover, we investigate the oscillation of the second -#111;-#114;-#100;-#101;-#114; nonlinearneutral differential equations of the form: br I r 11 br (r(t)tif (x(t))(x(t) + p(t)x(o-(t)))) +q (t) f (x(t),x(r (t)))=0, t r°. br j =1 br Finally, we discuss the stability character of the second -#111;-#114;-#100;-#101;-#114; nonlinear differential equation of the form: br x”+ h(t , x’) + x + g(t,x)=0, t E R. br The obtained |