Existence and uniqueness of positive periodic solutions for a class of integral equations with parameters

Volume 96 / 2009

Shu-Gui Kang, Bao Shi, Sui Sun Cheng Annales Polonici Mathematici 96 (2009), 227-238 MSC: Primary 45M15; Secondary 45M05. DOI: 10.4064/ap96-3-3


Existence of periodic solutions of functional differential equations with parameters such as Nicholson's blowflies model call for the investigation of integral equations with parameters defined over spaces with periodic structures. In this paper, we study one such equation $$ \phi (x)=\lambda \int_{\lbrack x,x+\omega ]\cap {\mit\Omega} } K(x,y)h(y)f(y,\phi(y-\tau(y)))\,dy,\quad x\in{\mit\Omega}, $$ by means of the proper value theory of operators in Banach spaces with cones. Existence, uniqueness and continuous dependence of proper solutions are established.


  • Shu-Gui KangCollege of Mathematics and Computer Science
    Shanxi Datong University
    Datong, Shanxi 037009, P.R. China
  • Bao ShiDepartment of Basic Sciences
    Naval Aeronautical Engineering Institute
    Yantai, Shandong 264001, P.R. China
  • Sui Sun ChengDepartment of Mathematics
    Tsing Hua University
    Hsinchu, Taiwan 30043, R. O. China

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