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

Shu-Gui Kang, Bao Shi, and Sui Sun Cheng. "Existence and uniqueness of positive periodic solutions for a class of integral equations with parameters." Annales Polonici Mathematici 96.3 (2009): 227-238. <http://eudml.org/doc/280961>.

@article{Shu2009,
abstract = {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 $ϕ(x) = λ∫_\{[x,x+ω]∩Ω\} K(x,y)h(y)f(y,ϕ(y-τ(y)))dy$, x ∈ Ω, by means of the proper value theory of operators in Banach spaces with cones. Existence, uniqueness and continuous dependence of proper solutions are established.},
author = {Shu-Gui Kang, Bao Shi, Sui Sun Cheng},
journal = {Annales Polonici Mathematici},
keywords = {periodic solutions; monotone operators; positive solutions; parameter-dependent integral equations},
language = {eng},
number = {3},
pages = {227-238},
title = {Existence and uniqueness of positive periodic solutions for a class of integral equations with parameters},
url = {http://eudml.org/doc/280961},
volume = {96},
year = {2009},
}

TY - JOUR
AU - Shu-Gui Kang
AU - Bao Shi
AU - Sui Sun Cheng
TI - Existence and uniqueness of positive periodic solutions for a class of integral equations with parameters
JO - Annales Polonici Mathematici
PY - 2009
VL - 96
IS - 3
SP - 227
EP - 238
AB - 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 $ϕ(x) = λ∫_{[x,x+ω]∩Ω} K(x,y)h(y)f(y,ϕ(y-τ(y)))dy$, x ∈ Ω, by means of the proper value theory of operators in Banach spaces with cones. Existence, uniqueness and continuous dependence of proper solutions are established.
LA - eng
KW - periodic solutions; monotone operators; positive solutions; parameter-dependent integral equations
UR - http://eudml.org/doc/280961
ER -