Pseudo Almost Periodic Solution For Nonlinear Differential Equations With Delays

In this paper, we study the existence and uniqueness of pseudo almost periodic solution and bounded solution for a nonlinear differential equation with delay(?)(t)-x(t)+g(t.x(t-r))=f(t),where f(t) is pseudo almost periodic or bounded continuous and r≥0, obtaining results of existence and uniqueness of these two solutions for equation (2.1.1) (See Theorems 3.1.1 and 3.1.2). As special cases of our main result (Theorem 3.1.1), we present the existence and uniqueness corollaries (See Corollary 3.2.1, Corollary 3.2.2, and Corollary 3.2.3) of the equation, in the conditions of f, g are almost periodic, qusi-periodic and periodic, respectively. Theorem 3.1.2 and Corollary 3.2.1 generalize and improve the results of Theorems 1, 2 in [6] of Wang. Therefore, compared to some known related results, our results could be applied more extensively.