In this paper the asymptotic behavior for all nonoscillatory solutions of third order nonlinear neutral differential equations have been investigated, where some necessary and sufficient conditions are obtained to guarantee the convergence of these solutions to zero or tends to infinity as t → ∞. We introduced Lemma 2.1 and Lemma 2.2 which are a generalization of Lemma 1.5.2 [I.

In this paper some necessary and sufficient conditions of n – th order neutral differential equations are obtained to insure the convergence of all nonoscillatory solutions to zero or tends to infinity as t → ∞. Some examples are given to illustrate the main results.

Some necessary and sufficient conditions are obtained that guarantee the oscillation of all solutions of two types of neutral integro-differential equations of third order. The integral is used in the sense of Riemann-Stieltjes. Some examples were included to illustrate the obtained results

The preset paper aims at finding the complete solution of certain types of linear partial differential equations of third order with constant coefficients that have three independent variables (q, r, s) of the general form: A 1 G q q q + A 2 G q q r + A 3 G q r r + A 4 G q r r + A 4 G r r r + A 5 G q q s + A 6 G q s s + A 7 G q r s + A 8 G r r s + A 9 G r s s + A 10 G s s s + A 11 G q q + A 12 G q r + A 13 G q s + A 14 G r r + A 15 G r s + A 16 G s s + A 17 G q + A 18 G r + A 19 G s + A 20 G = 0 By using the assumption: G(q,r,s) = e ∫y(q)dq + ∫x(r)dr + z(s)ds , the above equation, according to this assumption, will be transformed to the non-linear second order ordinary differential equation with three independent functions. Thus, they have the general form: A 1 ( y ″ + 3 y y ′ + y 3 ) + A 2 ( x y ′ + x y 2 ) + A 3 ( y x ′ + y x 2 ) + A 4 ( x ″ + 3 x x ′ + x 3 ) + A 5 ( z y ′ + z y 2 ) + A 6 ( y z ′ + y z 2 ) + A 7 y x z + A 8 ( z x ′ + z x 2 ) + A 9 ( x z ′ + x z 2 ) + A 10 ( z ″ + 3 z z ′ + z 3 ) + A 11 ( y ′ + y 2 ) + A 12

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