Abstract
In this paper, a thorough analysis of the existence and uniqueness of periodic solutions for a class of pth order neutral differential equations (NDE) with some delays is presented. Using Fourier series theory and techniques of real analysis inequality, a set of new and leading significance sufficient conditions are obtained ensuring the existence and uniqueness of periodic solutions. Thus some previous results [Appl. Math. J. Chinese Univ. 8A(3) (1993) 251 (in Chinese); Pure Appl. Math. 12(2) (1996) 69 (in Chinese); Pure Appl. Math. 11(suppl.) (1995) 102 (in Chinese); Appl. Math. Mech. 17(1) (1996) 29; Appl. Math. Mech. 20(6) (1999) 647] are extended and improved much more. Moreover, the repeated and ingenious application of inequality techniques makes the conditions of our results become weaker and weaker. Therefore, the conditions possess highly important significance in both theories and applications. In addition, the methods of this paper may be extended to study some other systems.
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