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

Shu-Gui Kang, Bao Shi, Sui Sun Cheng (2009)

Annales Polonici Mathematici

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 ) ) ) d y , 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.

Existence for nonconvex integral inclusions via fixed points

Aurelian Cernea (2003)

Archivum Mathematicum

We consider a nonconvex integral inclusion and we prove a Filippov type existence theorem by using an appropiate norm on the space of selections of the multifunction and a contraction principle for set-valued maps.

Existence of solutions for integrodifferential inclusions in Banach spaces

Nikolaos S. Papageorgiou (1991)

Commentationes Mathematicae Universitatis Carolinae

In this paper we examine nonlinear integrodifferential inclusions defined in a separable Banach space. Using a compactness type hypothesis involving the ball measure of noncompactness, we establish two existence results. One involving convex-valued orientor fields and the other nonconvex valued ones.

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