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. 
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     author = {Alessio, Francesca and Caldiroli, Paolo and Montecchiari, Piero},
     title = {On the existence of infinitely many solutions for a class of semilinear elliptic equations in \( {\mathbb{R}^{N}} \)},
     journal = {Atti della Accademia nazionale dei Lincei. Rendiconti Lincei. Matematica e applicazioni},
     pages = {157--165},
     publisher = {mathdoc},
     volume = {Ser. 9, 9},
     number = {3},
     year = {1998},
     zbl = {0923.35057},
     mrnumber = {MR1683006},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/RLIN_1998_9_9_3_a2/}
}
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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/