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Solution of the 1 : −2 resonant center problem in the quadratic case

Alexandra Fronville, Anton Sadovski, Henryk Żołądek (1998)

Fundamenta Mathematicae

The 1:-2 resonant center problem in the quadratic case is to find necessary and sufficient conditions (on the coefficients) for the existence of a local analytic first integral for the vector field ( x + A 1 x 2 + B 1 x y + C y 2 ) x + ( - 2 y + D x 2 + A 2 x y + B 2 y 2 ) y . There are twenty cases of center. Their necessity was proved in [4] using factorization of polynomials with integer coefficients modulo prime numbers. Here we show that, in each of the twenty cases found in [4], there is an analytic first integral. We develop a new method of investigation of analytic...

Solution sets of multivalued Sturm-Liouville problems in Banach spaces

Alessandro Margheri, Pietro Zecca (1994)

Atti della Accademia Nazionale dei Lincei. Classe di Scienze Fisiche, Matematiche e Naturali. Rendiconti Lincei. Matematica e Applicazioni

We give some results about the topological structure of solution sets of multivalued Sturm-Liouville problems in Banach spaces.

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