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Esistenza di infinite soluzioni per problemi non lineari in assenza di parametro

Antonio Ambrosetti — 1972

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

Consider the variational, non-linear boundary value problem i , k x i ( a i , k ( x ) u x k ) + ψ ( x , u ( x ) ) = 0    u | Ω = 0 in a bounded open set Ω 𝐑 n . If a i , k ( x ) and ψ ( x , t ) satisfy suitable conditions (see § 1), we prove that (1) has an infinite number of solutions, which are the critical points of a functional on a suitable manifold. This critical points are studied by means of Lusternik-Schnirelman theory.

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