On a Lyapunov-Type Inequality for Control of a ψ-Model Thermostat and the Existence of Its Solutions

Shahram Rezapour, Sina Etemad, Ravi P. Agarwal, Kamsing Nonlaopon

Type: Article

Publication Date: 2022-10-30

Citations: 8

DOI: https://doi.org/10.3390/math10214023

Abstract

In this paper, a new structure of an applied model of thermostat is defined using the generalized ψ-operators with three-point boundary conditions. Some useful properties of the relevant Green’s function are established, and based on these properties, the Lyapunov-type inequality is constructed for the given extended ψ-model thermostat with the help of Jensen’s inequality. By defining mild solutions for such an extended system, the existence and non-existence conditions are discussed.

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