On the shape of solutions of an asymptotically linear problem
Annali della Scuola Normale Superiore di Pisa - Classe di Scienze, Serie 5, Volume 8 (2009) no. 3, p. 429-449

In this paper we study the problem $\left(0.1\right)\phantom{\rule{1em}{0ex}}\left\{\begin{array}{cc}-\Delta u={|u|}^{ϵ}u\hfill & \phantom{\rule{4pt}{0ex}}\text{in}\phantom{\rule{4pt}{0ex}}\Omega \hfill \\ u=0\hfill & \phantom{\rule{4pt}{0ex}}\text{on}\phantom{\rule{4pt}{0ex}}\partial \Omega \hfill \end{array}\right\$where $\Omega$ is a smooth bounded domain of ${ℝ}^{N}$, $N\ge 1$, $ϵ>0$. We will show that, under some assumptions, the solutions to (0.1) are close to suitable linear combinations of eigenfunctions of the problem$\left\{\begin{array}{cc}-\Delta u=\lambda u\hfill & \phantom{\rule{4pt}{0ex}}\text{in}\phantom{\rule{4pt}{0ex}}\Omega \hfill \\ u=0\hfill & \phantom{\rule{4pt}{0ex}}\text{on}\phantom{\rule{4pt}{0ex}}\partial \Omega \hfill \end{array}\right\$.

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, Serie 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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