Detecting Initial Data Generating (b, c)-Bounded Solutions of Scalar Non-Homogeneous Linear Discrete Equations

Detecting Initial Data Generating (b, c)-Bounded Solutions of Scalar Non-Homogeneous Linear Discrete Equations

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The paper is concerned with the scalar linear non-homogeneous equation u(k + 1) = (1 + φ(k))u(k) + δ(k), k = k0, k0 + 1,..., where k0 is a fixed integer, φ(k) and δ(k) are real functions, and u(k) is an unknown real function. Sufficient conditions are given guaranteeing that the particular solution, generated by a constructed initial value u(k0) is (b, c)-bounded, i.e., for given functions b(k), c(k) satisfying b(k) < c(k) for k = k0, k0 + 1,..., the inequalities b(k) < u(k) < c(k), k = k0, k0 + 1,... hold. The sufficient conditions presented here differ from those known previously.

The paper is concerned with the scalar linear non-homogeneous equation u(k + 1) = (1 + φ(k))u(k) + δ(k), k = k0, k0 + 1,..., where k0 is a fixed integer, φ(k) and δ(k) are real functions, and u(k) is an unknown real function. Sufficient conditions are given guaranteeing that the particular solution, generated by a constructed initial value u(k0) is (b, c)-bounded, i.e., for given functions b(k), c(k) satisfying b(k) < c(k) for k = k0, k0 + 1,..., the inequalities b(k) < u(k) < c(k), k = k0, k0 + 1,... hold. The sufficient conditions presented here differ from those known previously.

Initial Data, Bounded Solution, Discrete Equation, Scalar Linear Equation.

Initial Data, Bounded Solution, Discrete Equation, Scalar Linear Equation.

DIBLÍK, J.

2026

11.09.2025

American Institute of Physics

USA

9780735452459

AIP Conf. Proc. 3315, 260002 (2025)

AIP conference proceedings

Spojené státy americké

260003-1

260003-4

4

https://pubs.aip.org/aip/acp/article-abstract/3315/1/260003/3363141/Detecting-initial-data-generating-b-c-bounded?redirectedFrom=fulltext