my study Data is measuring the macroeconomic variables in different location when I'm checking my study Data I found it non-stationary for each location and then initiated those first differences it become stationary. Can I use linear mixed models in such a situation? Are there any studies on this subject?
What do you mean by non-stationary data? Do you mean violation of these conditions (https://en.wikipedia.org/wiki/Stationary_process) ?
It depends on your data, actually. Number of changes, strength of effect in each segment, etc.
You can divide your data into stationary segments and then apply GLMM inside these segments, and there is methods for such segments detection. Also you can fit LOESS regression to your data and normalize it.
https://en.wikipedia.org/wiki/Change_detection
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