A researcher have to work to afford living, and the work institution does not encourage research that much, but he or she likes research and publishing the work in open access reputable journals, what do you advise?
I think that you should apply to international funding agencies for support of your research. There are funding agencies that are not affiliated with a specific institution, but work internationally.
for me it is a very good sign if a company/ institution is interested in the research. it implies the research has a lot of practical worth. what to do next depends on whether it is a profit or not for profit you are referring to.
what is the research about? if it has worth, as seems to be the case, someone would be willing to fund it. it is merely a case of finding/ speaking to the right person
I think that you should apply to international funding agencies for support of your research. There are funding agencies that are not affiliated with a specific institution, but work internationally.
I am interested in many areas in applied mathematics like Fuzzy Control of nonlinear systems, Approximate-Analytical methods and Numerical Methods to find solution to pde and ode. many thanks for the help Avishag Gordon.
The funding agencies in your area of research are mostly Chinese, these days, the agency that is not affiliated with one institution is Fundamental Research Funds for the Central Universities
National Natural Science Foundation of China
There are more agencies, almost all of them from China but they are related to a specific province there.
There is also the American NSF but they usually demand that your research will be done in the USA. It seems, though, that in your research area today, the main funding agencies are Chinese.
In many cases, you do not have to pay any fees if you agree that your article is NOT published open access but of course you should check each journal specifically for that.
Note that many Springer journals let you share your article via ReadCube so that it can be read by anyone (but cannot be downloaded if one has no valid subscription) who has a sufficiently modern browser to handle enhanced PDF; for example the published version of my recent article Integrable (3+1)-dimensional systems with rational Lax pairs can be read in this way here: http://rdcu.be/Dkwh .
This can be a reasonable substitute for open access (of course, if you are NOT officially required to publish open access by, say, your university or your grant agency), but again you should check this for each journal separately whether this feature is available for it; see also https://www.springernature.com/gp/researchers/sharedit for details.
Also, many journals allow the authors to post a preprint version of their article on their personal web site or at a repository like arXiv.org but again you should check each journal specifically for that (and for the exact definition of what does this particular journal mean by a preprint). This is commonly known as self-archiving or green open access. Of course, this probably would NOT suffice if you are officially required to publish open access by, say, your university or your grant agency .
In my view, I think the open access publication option should be eliminated for a number of reasons. First, certain publication will gain large number of citations if it presents novel high value approach. Second, nowadays most of the accredited institutions provide access to journals so the publications will be available for researchers.