Bounded Solutions of a Triangular System of Two Nonlinear Discrete Equations

Bounded Solutions of a Triangular System of Two Nonlinear Discrete Equations

Stať ve sborníku v databázi WoS či Scopus

A nonlinear triangular system of discrete equations u_1(k + 1) = q_1(k)u^p_1 (k), u_2(k + 1) = q_2(k)u^r_1(k)u^t_2(k) is considered where q_i: {a, a + 1,...} → (0, ∞), i = 1, 2 are given functions, a is a fixed positive integer and p, r, t are positive numbers. Sufficient conditions are given for the existence of a solution u = (u_1, u_2): {a, a + 1,...} → R × R such that its coordinates u_i, i = 1, 2 are between two given functions b_i, c_i: {a, a + 1,...} → R satisfying 0 ≤ b_i(k) < c_i(k) for every k ∈ {a, a + 1,...}.

A nonlinear triangular system of discrete equations u_1(k + 1) = q_1(k)u^p_1 (k), u_2(k + 1) = q_2(k)u^r_1(k)u^t_2(k) is considered where q_i: {a, a + 1,...} → (0, ∞), i = 1, 2 are given functions, a is a fixed positive integer and p, r, t are positive numbers. Sufficient conditions are given for the existence of a solution u = (u_1, u_2): {a, a + 1,...} → R × R such that its coordinates u_i, i = 1, 2 are between two given functions b_i, c_i: {a, a + 1,...} → R satisfying 0 ≤ b_i(k) < c_i(k) for every k ∈ {a, a + 1,...}.

nonlinear system; triangular system; discrete equation; retract method.

nonlinear system; triangular system; discrete equation; retract method.

BAŠTINEC, J.; DIBLÍK, J.; KOROBKO, E.

2022

06.04.2022

AIP

Melville (USA)

978-0-7354-4182-8

ICNAAM 2020 PROCEEDINGS - AIP CP Volume 2425

0094-243X

AIP conference proceedings

2245

1

Spojené státy americké

270008-1

270008-4

4

https://doi.org/10.1063/5.0081826