no. 3
On the shape of solutions of an asymptotically linear problem
Grossi, Massimo1
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.

In this paper we study the problem ( 0 . 1 ) - Δ u = | u | ϵ u in Ω u = 0 on ∂ Ω where Ω is a smooth bounded domain of ℝ N , N ≥ 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 - Δ u = λ u in Ω u = 0 on ∂ Ω .

Classification : 35J60
Grossi, Massimo 1

1 Dipartimento di Matematica, Sapienza Università di Roma, Piazzale A. Moro, 2, 00185 Roma, Italia 
@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},
     pages = {429--449},
     publisher = {Scuola Normale Superiore, Pisa},
     volume = {Ser. 5, 8},
     number = {3},
     year = {2009},
     mrnumber = {2574338},
     zbl = {1182.35116},
     language = {en},
     url = {http://archive.numdam.org/item/ASNSP_2009_5_8_3_429_0/}
}
TY  - JOUR
AU  - Grossi, Massimo
TI  - On the shape of solutions of an asymptotically linear problem
JO  - Annali della Scuola Normale Superiore di Pisa - Classe di Scienze
PY  - 2009
SP  - 429
EP  - 449
VL  - 8
IS  - 3
PB  - Scuola Normale Superiore, Pisa
UR  - http://archive.numdam.org/item/ASNSP_2009_5_8_3_429_0/
LA  - en
ID  - ASNSP_2009_5_8_3_429_0
ER  - 
%0 Journal Article
%A Grossi, Massimo
%T On the shape of solutions of an asymptotically linear problem
%J Annali della Scuola Normale Superiore di Pisa - Classe di Scienze
%D 2009
%P 429-449
%V 8
%N 3
%I Scuola Normale Superiore, Pisa
%U http://archive.numdam.org/item/ASNSP_2009_5_8_3_429_0/
%G en
%F 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, Tome 8 (2009) no. 3, pp. 429-449. http://archive.numdam.org/item/ASNSP_2009_5_8_3_429_0/

[1] D. Bonheure, V. Bouchez, C. Grumiau and J. Van Schaftingen, Asymptotics and symmetries of least energy nodal solutions of Lane-Emden problems with slow growth, Commun. Contemp. Math. 10 (2008), 1–23. | MR | Zbl

[2] D. C. Clark, A variant of the Lusternik-Schnirelman theory, Indiana Univ. Math. J. 22 (1972/73), 65–74. | MR | Zbl

[3] E. N. Dancer, Real analyticity and non-degeneracy, Math. Ann. 325 (2003), 369–392. | MR | Zbl

[4] E. N. Dancer, Y. Du and L. Ma, Asymptotic behavior of positive solutions of some elliptic problems, Pacific J. Math. 210 (2003), 215–228. | MR | Zbl

[5] C. S. Lin, Uniqueness of least energy solutions to a semilinear elliptic equation in R 2 , Manuscripta Math. 84 (1994), 13–19. | EuDML | MR | Zbl

[6] A. M. Micheletti, Perturbazione dello spettro dell’operatore di Laplace, in relazione ad una variazione del campo, Ann. Scuola Norm. Sup. Pisa Cl. Sci. 26 (1972), 151–169. | EuDML | Numdam | MR

[7] P. H. Rabinowitz, “Minimax Methods in Critical Point Theory with Applications to Differential Equations”, CBMS Regional Conference Series in Mathematics, Amer. Math. Soc., Vol. 65, Providence RI, 1986. | MR | Zbl

[8] K. Uhlenbeck, Generic properties of eigenfunctions, Amer. J. Math. 98 (1976), 1059–1078. | MR | Zbl