Oscillatory and Asymptotic Behavior of First Order Functional Differential Equations

In this paper the author discusses the following first order functional differential equations:$x''(t)+[int_a^b {p(t,xi )x[g(t,xi )]dsigma (xi ) = 0} ] (1)$$x''(t)+[int_a^b {f(t,xi )x[g(t,xi )]dsigma (xi ) = 0} ] (2)$Some sufficient conditions of oscillation and nonoscillation are obtained, and two asymptotic properties and their criteria are given. These criteria are better than those in [1, 2], and can be used to the following equations:$x''(t)+[sumlimits_{i = 1}^n {{p_i}(t)x[{g_i}(t)] = 0} ] (3)$$x''(t)+[sumlimits_{i = 1}^n {{f_i}(t)x[{g_i}(t)] = 0} ] (4)$