The phrase "assumption of existing" is not correct and does not convey a clear meaning in written English.
It may be intended to refer to the acceptance or acknowledgment of something that already exists, but it lacks clarity and context.
Example: "The assumption of existing conditions must be taken into account when planning the project."
Alternatives: "acknowledgment of existing" or "recognition of existing".
In the above-mentioned papers, main results are formulated and proved under the assumption of existing upper and lower solutions in the usual order.
In 2009, Wang et al. [27] successfully investigated boundary value problem for functional differential equations without impulses under the assumption of existing upper and lower solutions in the reversed order.
In this paper, we have discussed the integral boundary value problem for first-order impulsive functional integrodifferential equations with deviating arguments under the assumption of existing upper and lower solutions in the reversed order.
This paper investigates the existence of the extremal solutions to the integral boundary value problem for first-order impulsive functional integrodifferential equations with deviating arguments under the assumption of existing upper and lower solutions in the reversed order.
As far as I am concerned, no paper has considered first-order impulsive functional integrodifferential equations with integral boundary conditions and deviating arguments (i.e., problem (1.1)) under the assumption of existing upper and lower solutions in the reverse order.
Finally, the assumptions of existing policies and programmes designed to help teachers to bridge the theory-practice gap are enacted as intended have to be reexamined.
In particular, assumptions of existing models of the acoustic effect of perforated plate are assessed thanks to the Large-Eddy Simulations results.
The comparison shows, that the assumptions of existing models are by far too simple and the models are therefore not applicable for technological relevant electrochemical devices.
Results of the experiments show that the proposed system can work under bursts of packet loss and ambient wireless traffic levels which are intolerable for basic networked control systems while not being hindered by restraining assumptions of existing methods.
The analytical methodology presented herein maintains the well-established assumptions of existing methodologies, but also introduces a number of refinements in order to achieve a more wide range of application without any major simplicity sacrifice.
All models were developed based on assumptions of existing and near - term cellulosic ethanol production technologies.
