Geodesic
Analytic solutions to nonlocal abstract equations
Bollettino della Unione matematica italiana, Série 8, 6B (2003) no. 1, pp. 181-198.

Voir la notice de l'article provenant de la source Biblioteca Digitale Italiana di Matematica

In this paper we study the problem of existence of global solutions for some classes of abstract equations, that generalize some type of Klein-Gordon equations, with nonlinear nonlocal terms of Kirchhoff type. We find some conditions that guarantee the existence of such solutions whether in presence or in absence of a conserved energy.
Si considera il problema dell'esistenza di soluzioni globali analitiche per equazioni astratte, in spazi di Hilbert, di tipo Klein-Gordon corrette con termini non locali, del tipo: $$u''+ m(\|u \|^{2}_{H}, \langle Au,u \rangle ) Au + n(\|u \|^{2}_{H}, \langle Au,u \rangle)u=0 .$$ In particolare si individuano classi di condizioni sulle funzioni m ed n (sia in presenza che in assenza di energie conservate) che garantiscono l'esistenza di tali soluzioni. 
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Ghisi, Marina. Analytic solutions to nonlocal abstract equations. Bollettino della Unione matematica italiana, Série 8, 6B (2003) no. 1, pp. 181-198. https://geodesic-test.mathdoc.fr/item/BUMI_2003_8_6B_1_a10/

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