Periodic Solutions And Stability Of Neutral Functional Differential Equations

This thesis is concerned with periodic solutions of neutral functional differential equations and asymptotic stability. The thesis contains four chapters.In Chapter-1, we introduce periodic differential equations and periodic solutions of periodic equations, we also introduce the neutral equationand give the stability definitions of the equation's zero solutin, and the main results of the thesis.In Chapter-2, a class of first order nonlinear differential equationsx'(t) = f(t, x(t), x(t - Ï„₁),x(t - Ï„₂),x'(t - Ï„₁), x'(t - Ï„₂)) + p(t)are considered, we discuss the existence of periodic solutions. By using the abstract continuity theorem, we obtain sufficient conditions for the existence of periodic solutions related with delays, and An example is given to illustrate the main results.In Chapter-3, we discuss the following nonlinear neutral delay equation:[x(t) + cx(t - Ï„)]" + f(t, x(t - ω₁)) + g(t, x(t - ω₂)) = p(t)By using the coincidence degree theory, we obtain the existence of periodic solutions. An example is given to illustrate the main results.In Chapter-4, we discuss the stability of a class of linear neutral differential equations:...