an:01631169
Zbl 0981.45002
Li, Yongkun; Xu, Guitong
Positive periodic solutions for an integrodifferential model of mutualism
EN
Appl. Math. Lett. 14, No. 5, 525-530 (2001).
00075005
2001
j
45J05 45M15 45M20 92D25 45G15 92D40
nonlinear integro-differential equations; positive periodic solution; continuation theorem; mutualism; Fredholm operator
The paper deals with a system of two nonlinear integro-differential equations of first order which presents a model of mutualism. The ecological meaning of such type systems may be found in the book by \textit{K. Gopalsamy} [Stability and oscillations in delay differential equations of population dynamics (1992; Zbl 0752.34039)]. Sufficient conditions are given for the existence of at least one positive periodic solution of the system under consideration. The proof is based on the continuation theorem on the existence of at least one solution of the operator equation with Fredholm operator of index zero; in this connection see the book by \textit{R. E. Gaines} and \textit{J. L. Mawhin} [Coincidence degree and nonlinear differential equations (1977; Zbl 0339.47031)].
Anatoliy Aleksandrovich Kilbas (Minsk)
Zbl 0752.34039; Zbl 0339.47031