If I prepare the silver nitrate solution or any other solution, how can I know the shelf life of this solution? I know that it depends on the stability of the substance, but maybe there is some document which give information and is interesning how realy it was found.
You won't find a general formula for the shelf life of a solution. A silver nitrate solution will have a very short shelf life if it is kept in the sunlight, whereas potassium nitrate could last for years. The shelf life is also going to be very strongly dependent on the quality of the container. Think about what happens to the aging of a wine bottle if the cork does not provide a sufficient seal . Interactions between the solution and the container have an impact on the solution shelf life as well. To stick with the wine theme, corked wine is due to contamination of the wine with 2,4,6-trichloroanisole which is generated by natural fungi in the cork that have been exposed to chlorine.
So it is important to understand the chemistry of the solution with which you are working in order to determine its shelf life.