Existence of positive bounded solutions of system of three dynamic equations with neutral term on time scales

Rok, strany: 2019, 123 - 137

In this paper, the system of three dynamic equations with neutral term in the following form \begin{equation*} \begin{cases} & (x(t)+p(t) \, x(u_1(t)))^{\Delta} = a(t) \, f(y(u_2(t))), \\ & y^{\Delta}(t)= b(t) \, g(z(u_3(t))), \\ & z^{\Delta}(t)= c(t)\, h(x(u_4(t))) \end{cases} \end{equation*} on time scales is considered. The aim of this paper is to present sufficient conditions for the existence of positive bounded solutions of the considered system for $0 < p(t) \leq const < 1$. The main tool of the proof of presented here result is Krasnoselskii's fixed point theorem. Also, the useful generalization of the Arzel{\'a}-Ascoli theorem on time scales to the three-dimensional case is proved.

ISO 690:

Ostaszewska, U., Schmeidel, E., Zdanowicz, M. 2019. Existence of positive bounded solutions of system of three dynamic equations with neutral term on time scales. In Tatra Mountains Mathematical Publications, vol. 71, no.1, pp. 123-137. 1210-3195. DOI: https://doi.org/10.2478/tmmp-2018-0011

APA:

Ostaszewska, U., Schmeidel, E., Zdanowicz, M. (2019). Existence of positive bounded solutions of system of three dynamic equations with neutral term on time scales. Tatra Mountains Mathematical Publications, 71(1), 123-137. 1210-3195. DOI: https://doi.org/10.2478/tmmp-2018-0011

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