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This paper deals with a class of two-dimensional linear differential systems with periodic coefficients. A sufficient condition for the exponential dichotomy of the linear system is given by the fixed point theorem and variable substitution, and some new results are obtained.

This paper deals with a class of one element n-degree polynomial differential equations. By the fixed point theory, we obtain n periodic solutions of the equation. This paper generalizes some related conclusions of some papers.

In this paper, the existence of a periodic solution for Abel’s differential equation is obtained first by using the fixed-point theorem. Then, by constructing the Lyapunov function, the uniqueness and stability of the periodic solution of the equation are obtained.

This paper deals with a nonlinear differential equation, by using the fixed point theory. The existence of the periodic solution of the nonlinear differential equation is obtained; these results are new.

With the help of the variable substitution and applying the fixed point theorem, we derive the sufficient conditions which guarantee the existence of the positive almost periodic solutions for a class of Lotka-Volterra type system. The main results improve and generalize the former corresponding results.

This paper deals with a first-order differential equation with a polynomial nonlinear term. The integrability and existence of periodic solutions of the equation are obtained, and the stability of periodic solutions of the equation is derived.

We study the following nonlinear equationdx(t)/dt=x(t)[a(t)-b(t)xα(t)-f(t,x(t))]+g(t), by using fixed point theorem, the sufficient conditions of the existence of a unique positive almost periodic solution for above system are obtained, by using the theories of stability, the sufficient conditions which guarantee the stability of the unique positive almost periodic solution are derived.