Geodesic
On the existence of infinitely many solutions for a class of semilinear elliptic equations in \( \mathbb{R}^{N} \)
Atti della Accademia nazionale dei Lincei. Rendiconti Lincei. Matematica e applicazioni, Série 9, Tome 9 (1998) no. 3, pp. 157-165.

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

We show, by variational methods, that there exists a set \( \mathcal{A} \) open and dense in \( {a \in L^{\infty} ( \mathbb{R}^{N}) : a \ge 0} \) such that if \( a \in \mathcal{A} \) then the problem \( - \triangle u + u = a(x) |u|^{p-1} u, u \in H^{1}(\mathcal{R}^{N}) \), with \( p \) subcritical (or more general nonlinearities), admits infinitely many solutions.
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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     journal = {Atti della Accademia nazionale dei Lincei. Rendiconti Lincei. Matematica e applicazioni},
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Alessio, Francesca; Caldiroli, Paolo; Montecchiari, Piero. On the existence of infinitely many solutions for a class of semilinear elliptic equations in \( \mathbb{R}^{N} \). Atti della Accademia nazionale dei Lincei. Rendiconti Lincei. Matematica e applicazioni, Série 9, Tome 9 (1998) no. 3, pp. 157-165. http://geodesic.mathdoc.fr/item/RLIN_1998_9_9_3_a2/

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