The phrase "greatly demand" is correct and usable in written English.
You could use it when you want to emphasize the importance of something that is in high demand, or when you are referring to a situation in which the request for something is very great. For example, you could say: "This product has greatly demanded by consumers".
The high-performance nonvolatile memory is greatly demanded in modern information technology.
Economical and efficient long-distance oil and natural gas pipe transportation technologies are greatly demanded.
This kind of service is not sensitive to delay and jitter but greatly demands on data rate.
In this regard, synthesis of iron oxide nanoparticles with desirable properties and high potential applications are greatly demanded.
To fully understand its biological functions in cellular signaling pathways, apoptosis and human diseases, effective chemical tools for directly tracing HClO at subcellular levels are greatly demanded.
Manufactured foods are greatly demanded due to their cooking abilities; they can also be easily transported and therefore have greater access to markets, a situation which fosters greater market integration.
Moreover, monodisperse spherical and small phosphor particles prepared on a substrate are greatly demanded not only for improvement of luminescence performance and screen resolution, but also for technological applications, such as light emitting devices and flat panel displays.
Hence, diving is a typical example of movements which is performed against air resistance under the influence of gravity, so spatial perception of body position is greatly demanded.
In addition, novel biomarkers, especially the non-invasive biomarkers, are greatly demanded.
A reliable biomarker for nephrolithiasis which could predict earlier diagnosis, treatment, or better monitoring is greatly demanded.
