Alessio, Caldiroli, Montecchiari: On the existence of infinitely many solutions for a class of semilinear elliptic equations in \( \mathbb{R}^{N} \)

Alessio, Francesca and Caldiroli, Paolo and Montecchiari, Piero:
On the existence of infinitely many solutions for a class of semilinear elliptic equations in \( \mathbb{R}^{N} \) (Sull’esistenza di infinite soluzioni per una classe di equazioni ellittiche semilineari su \( \mathbb{R}^{N} \))
Atti della Accademia Nazionale dei Lincei. Classe di Scienze Fisiche, Matematiche e Naturali. Rendiconti Lincei. Matematica e Applicazioni Serie 9 9 (1998), fasc. n.3, p. 157-165, (English)
pdf (403 Kb), djvu (152 Kb). | MR1683006 | Zbl 0923.35057

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Usando metodi variazionali, si dimostra che esiste un insieme \( \mathcal{A} \) aperto e denso in \( {a \in L^{\infty} ( \mathbb{R}^{N}) : a \ge 0} \) tale che per ogni \( a \in \mathcal{A} \) il problema \( - \triangle u + u = a(x) |u|^{p-1} u, u \in H^{1}(\mathcal{R}^{N}) \), con \( p \) sottocritico (o con nonlinearità più generali), ammette infinite soluzioni.

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Referenze Bibliografiche