Existence of Nonoscillatory Solution of Second Order Linear Neutral Delay Equation

Consider the neutral delay differential equation with positive and negative coefficients, d2 dt2 ’xt‘ C pxt − ‘“ C Q1t‘xt − 1‘ − Q2t‘xt − 2‘ D 0; where p 2 R and 2 0;1‘; 1; 2 2 ’0;1‘ and Q1;Q2 2 C’t0;1‘;RC‘: Some sufficient conditions for the existence of a nonoscillatory solution of the above equation expressed in terms of R1 sQis‘ ds < 1, i D 1; 2; and certain technical conditions implying that Q1s‘ dominates Q2s‘ are obtained for values of p 6D 1.