The Australian Journal of Mathematical Analysis and Applications

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ISSN 1449-5910  


Paper Information

Paper Title:

Positive Periodic Solutions for Second-Order Differential Equations with Generalized Neutral Operator


Wing-Sum Cheung, Jingli Ren and Weiwei Han

Department of Mathematics,
The University of Hong Kong
 Pokfulam Road,
Hong Kong

Department of Mathematics, Zhengzhou University
Zhengzhou 450001,
P.R. China


By some analysis of the neutral operator and an application of the fixed-point index theorem, we obtain sufficient conditions for the existence, multiplicity and nonexistence of periodic solutions to a second-order differential equation with the prescribed neutral operator, which improve and extend some recent results of Lu-Ge, Wu-Wang, and Zhang. An example is given to illustrate our results. Moreover, the analysis of the generalized neutral operator will be helpful for other types of differential equations.


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