On the shape of solutions of an asymptotically linear problem

Grossi, Massimo

Grossi, Massimo ¹

¹ Dipartimento di Matematica, Sapienza Università di Roma, Piazzale A. Moro, 2, 00185 Roma, Italia

Annali della Scuola Normale Superiore di Pisa - Classe di Scienze, Série 5, Tome 8 (2009) no. 3, pp. 429-449.

Résumé

In this paper we study the problem $(0.1) \{\begin{matrix} - Δ u = {| u |}^{ϵ} u & in Ω \\ u = 0 & on \partial Ω \end{matrix}$ where $Ω$ is a smooth bounded domain of $ℝ^{N}$ , $N \geq 1$ , $ϵ > 0$ . We will show that, under some assumptions, the solutions to (0.1) are close to suitable linear combinations of eigenfunctions of the problem $\{\begin{matrix} - Δ u = λ u & in Ω \\ u = 0 & on \partial Ω \end{matrix}$ .

MR Zbl

Classification : 35J60

Affiliations des auteurs :

Grossi, Massimo ¹

¹ Dipartimento di Matematica, Sapienza Università di Roma, Piazzale A. Moro, 2, 00185 Roma, Italia

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     author = {Grossi, Massimo},
     title = {On the shape of solutions of an asymptotically linear problem},
     journal = {Annali della Scuola Normale Superiore di Pisa - Classe di Scienze},
     pages = {429--449},
     publisher = {Scuola Normale Superiore, Pisa},
     volume = {Ser. 5, 8},
     number = {3},
     year = {2009},
     mrnumber = {2574338},
     zbl = {1182.35116},
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     url = {http://www.numdam.org/item/ASNSP_2009_5_8_3_429_0/}
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Grossi, Massimo. On the shape of solutions of an asymptotically linear problem. Annali della Scuola Normale Superiore di Pisa - Classe di Scienze, Série 5, Tome 8 (2009) no. 3, pp. 429-449. http://www.numdam.org/item/ASNSP_2009_5_8_3_429_0/

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