Abstract:
In this paper, properties of solutions of the convolution-type integral equation (1+w(x))P(x)=(m∗P)(x)+Cm(x) on the real axis are studied. The main concern is to find conditions for the function w(x) and the kernel m(x) sufficient for the existence of an admissible solution P(x), i.e., a solution which has a nonzero limit at infinity. The main results of the paper are the uniqueness theorem for the admissible solution for rapidly decreasing kernels m and the existence theorem for one-sided compactly supported kernels m.
Citation:
V. I. Danchenko, R. V. Rubay, “On integral equations of stationary distributions for biological systems”, Proceedings of the Fifth International Conference on Differential and Functional-Differential Equations (Moscow, August 17–24, 2008). Part 2, CMFD, 36, PFUR, M., 2010, 50–60; Journal of Mathematical Sciences, 171:1 (2010), 34–45
\Bibitem{DanRub10}
\by V.~I.~Danchenko, R.~V.~Rubay
\paper On integral equations of stationary distributions for biological systems
\inbook Proceedings of the Fifth International Conference on Differential and Functional-Differential Equations (Moscow, August 17--24, 2008). Part~2
\serial CMFD
\yr 2010
\vol 36
\pages 50--60
\publ PFUR
\publaddr M.
\mathnet{http://mi.mathnet.ru/cmfd155}
\mathscinet{http://mathscinet.ams.org/mathscinet-getitem?mr=2752649}
\transl
\jour Journal of Mathematical Sciences
\yr 2010
\vol 171
\issue 1
\pages 34--45
\crossref{https://doi.org/10.1007/s10958-010-0124-6}
\isi{https://gateway.webofknowledge.com/gateway/Gateway.cgi?GWVersion=2&SrcApp=Publons&SrcAuth=Publons_CEL&DestLinkType=FullRecord&DestApp=WOS_CPL&KeyUT=000272756700004}
Linking options:
https://www.mathnet.ru/eng/cmfd155
https://www.mathnet.ru/eng/cmfd/v36/p50
This publication is cited in the following 2 articles:
A. A. Davydov, Kh. A. Khachatryan, “Statsionarnye sostoyaniya v dinamike populyatsii s migratsiei i raspredelennym potomstvom”, SMFN, 69, no. 4, Rossiiskii universitet druzhby narodov, M., 2023, 578–587
Kh.A. Khachatryan, H.S. Petrosyan, A. R. Hakobyan, “On solvability of one class of integral equations on whole line with monotonic and convex nonlinearity”, J Math Sci, 271:5 (2023), 610
Citation in format AMSBIB
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