一阶隐方程的周期解的存在性

EXISTENCE OF PERIODIC SOLUTIONS FOR FIRST ORDER IMPLICIT DIFFERENTIAL EQUATIONS

本文利用度理论及Ｆｒｅｄｈｏｌｍ算子研究了一阶隐方程ｘ＇＝ｆ（ｔ，ｘ，ｘ＇），ｘ（０）＝ｘ（２π）的周期解，广义周期解的存在性，得到了两个存在性定理，其中定理４．１推广了Ｊ．Ｊ．Ｎｉｅｔｏ［１］中的结果．

n this paper, we study the periodic boundary value problem for first order implicit differential equations by using degree theory and Fredholm operators. Two theorems about periodic solutions are obtained and one of them generalizes the main result in [1].