McKenna, P.J. and Shaw, Howard:
The structure of the solution set of some nonlinear problems
Atti della Accademia Nazionale dei Lincei. Classe di Scienze Fisiche, Matematiche e Naturali. Rendiconti Serie 8 65 (1978), fasc. n.6, p. 239-243, (English)
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Per equazioni operazionali $Lu + Nu = h$, $L$ ed $N$ operatori in uno spazio di Hilbert reale $X$, $L$ lineare, $N$ non lineare, e sotto moderate ipotesi su $L$ ed $N$, l'insieme delle soluzioni è, generalmente, una varietà di dimensione uguale all'indice di Fredholm di $L$. Precisamente, questo accade effettivamente se la proiezione di $h$ su un opportuno sottospazio $E$ di dimensione finita in $X$ non cade su un certo insieme $Z$ di $E$, di misura zero oppure di prima categoria.
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