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Advise me please some book on algebraic and differential Riccati equations: I'm interested in such questions as theorems of existence, uniqueness and extendibility of solutions of differential equation, explicit formulas for solutions and in related questions.

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Have you had a look at the references in the Wikipedia article? I can recommend Ince's book in particular. Since I don't have the book in front of me at the moment, I can't say whether it covers all of the topics you're interested in. –  Will Orrick May 31 '12 at 13:50
    
What do you mean by "algebraic Ricatti equation"? I know it as a differential and as a difference equation, but not algebraic. –  vonbrand Jan 24 '13 at 15:06
    
@vonbrand en.wikipedia.org/wiki/Algebraic_Riccati_equation –  Nimza Jan 24 '13 at 15:14
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