Geodesic
Existence and uniqueness of positive periodic solutions for a class of integral equations with parameters
Shu-Gui Kang1 ; Bao Shi2 ; Sui Sun Cheng3
1College of Mathematics and Computer Science Shanxi Datong University Datong, Shanxi 037009, P.R. China
2Department of Basic Sciences Naval Aeronautical Engineering Institute Yantai, Shandong 264001, P.R. China
3Department of Mathematics Tsing Hua University Hsinchu, Taiwan 30043, R. O. China
Annales Polonici Mathematici, Tome 96 (2009) no. 3, pp. 227-238
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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.
DOI : 10.4064/ap96-3-3
Keywords: existence periodic solutions functional differential equations parameters nicholsons blowflies model call investigation integral equations parameters defined spaces periodic structures paper study equation phi lambda int lbrack omega cap mit omega h phi y tau quad mit omega means proper value theory operators banach spaces cones existence uniqueness continuous dependence proper solutions established

Shu-Gui Kang  1   ; Bao Shi  2   ; Sui Sun Cheng  3

1 College of Mathematics and Computer Science Shanxi Datong University Datong, Shanxi 037009, P.R. China
2 Department of Basic Sciences Naval Aeronautical Engineering Institute Yantai, Shandong 264001, P.R. China
3 Department of Mathematics Tsing Hua University Hsinchu, Taiwan 30043, R. O. China 
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     title = {Existence and uniqueness of positive periodic solutions
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Shu-Gui Kang; Bao Shi; Sui Sun Cheng. Existence and uniqueness of positive periodic solutions
 for a class of integral equations with parameters. Annales Polonici Mathematici, Tome 96 (2009) no. 3, pp. 227-238. doi: 10.4064/ap96-3-3

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