The standard BibTeX abbreviations should not be given in braces, but bare as in
month = mar,
only then does BibTeX understand their special meaning.
You can read a bit about this in Tame the Beast where we find (on p. 13)
It's better having a numerical value, or an abbreviation, instead of the complete name of the month.
There it is not that clear that the abbreviation needs to be give without braces or quotation marks.
on p. 44 it says
Namely, for instance, months should be entered numerically.
So month = {jul}, is not the format recommended by Tame the Beast.
Have a look at the following BibTeX example
\documentclass{article}
\begin{filecontents}{\jobname.bib}
@article{Blavatskyy2011,
author = {Blavatskyy, Pavlo R.},
doi = {10.1287/mnsc.1100.1285},
month = mar,
number = {3},
pages = {542--548},
title = {{A Model of Probabilistic Choice Satisfying First-Order Stochastic Dominance}},
volume = {57},
year = {2011},
}
@article{bar,
author = {{The Pierre Auger Collaboration}},
eprint = {1107.4806},
journal = {ArXiv e-prints},
month = {jul},
title = {{The Pierre Auger Observatory IV: Operation and Monitoring}},
year = {2011}
}
\end{filecontents}
\begin{document}
These are my works, \cite{Blavatskyy2011,bar}
\bibliographystyle{plain}
\bibliography{\jobname}
\end{document}
The month wrapped in braces does not give the expected result.

The same holds if you use biblatex with the BibTeX back-end.
The new back-end Biber is so clever that it can even deal with braced month fields
So the following MWE will give the expected output (with backend=bibtex though, it won't work as expected).
\documentclass{article}
\usepackage[backend=biber]{biblatex}
\begin{filecontents}{\jobname.bib}
@article{Blavatskyy2011,
author = {Blavatskyy, Pavlo R.},
doi = {10.1287/mnsc.1100.1285},
month = mar,
number = {3},
pages = {542--548},
title = {{A Model of Probabilistic Choice Satisfying First-Order Stochastic Dominance}},
volume = {57},
year = {2011},
}
@article{bar,
author = {{The Pierre Auger Collaboration}},
eprint = {1107.4806},
journal = {ArXiv e-prints},
month = {jul},
title = {{The Pierre Auger Observatory IV: Operation and Monitoring}},
year = {2011}
}
\end{filecontents}
\addbibresource{\jobname.bib}
\begin{document}
These are my works, \cite{Blavatskyy2011,bar}
\printbibliography
\end{document}

Even though Biber has no problems with the file exported from Mendeley I still consider the export faulty, since BibTeX cannot properly deal with this.
So if you cannot change the .bib file and still want to get rid of the warnings you should try and use Biber.
.bibentry would be handy. For example, I wonder if you mean that it's creating string entries of the formmonth = jan, which can then be defined as@string{jan = "1"}. – Joseph Wright Jan 06 '16 at 09:32biblatexis thedatefield (inYYYY-MM-DDformat - you may of course leave out the day or the month and day). But you can use the fieldsyearandmonthfor backwards compatibility. (You can, however, not give the full date using adayfield, it will be ignored.) Would it be possible to show an example of what Mendeley exports? – moewe Jan 06 '16 at 16:03
– user95308 Jan 07 '16 at 02:58@article{bar, archivePrefix = {arXiv}, arxivId = {astro-ph.IM/1107.4806}, author = {{The Pierre Auger Collaboration}}, eprint = {1107.4806}, journal = {ArXiv e-prints}, keywords = {Astrophysics - High Energy Astrophysical Phenomena,Astrophysics - Instrumentation and Methods for Ast,High Energy Physics - Experiment,Physics - Instrumentation and Detectors}, month = {jul}, primaryClass = {astro-ph.IM}, title = {{The Pierre Auger Observatory IV: Operation and Monitoring}}, year = {2011} }BibTeX reported the following issues(biblatex) with 'bar':(biblatex) - Invalid format of field 'month'.
whereabouts could I place the
– user95308 Jan 07 '16 at 03:01@string{jan = "1"}macro?.bibexport is a bit meh and has some troubles, but I'm really confused why you getmonth = {jul},in the examples on this site if found the correctmonth = jul,. Unfortunately, when I import the paper in your example, I don't get a month at all. Anywaymonth = {jul},is not the correct output, you might want to complain to the Mendeley guys about this. If you use Biber I could come up with an ugly work-around. – moewe Jan 07 '16 at 06:59