On the shape of solutions of an asymptotically linear problem

Grossi, Massimo

Grossi, Massimo

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

Abstract

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 2574338 | Zbl 1182.35116

Classification: 35J60

@article{ASNSP_2009_5_8_3_429_0,
     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},
     publisher = {Scuola Normale Superiore, Pisa},
     volume = {Ser. 5, 8},
     number = {3},
     year = {2009},
     pages = {429-449},
     zbl = {1182.35116},
     mrnumber = {2574338},
     language = {en},
     url = {http://www.numdam.org/item/ASNSP_2009_5_8_3_429_0}
}

Grossi, Massimo. On the shape of solutions of an asymptotically linear problem. Annali della Scuola Normale Superiore di Pisa - Classe di Scienze, Série 5, Volume 8 (2009) no. 3, pp. 429-449. http://www.numdam.org/item/ASNSP_2009_5_8_3_429_0/

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