Non existence of bounded-energy solutions for some semilinear elliptic equations with a large parameter
Rendiconti del Seminario Matematico della Università di Padova, Volume 110 (2003), p. 147-160
@article{RSMUP_2003__110__147_0,
author = {Castorina, Daniele and Mancini, Gianni},
title = {Non existence of bounded-energy solutions for some semilinear elliptic equations with a large parameter},
journal = {Rendiconti del Seminario Matematico della Universit\a di Padova},
publisher = {Seminario Matematico of the University of Padua},
volume = {110},
year = {2003},
pages = {147-160},
zbl = {1121.35053},
mrnumber = {2033005},
language = {en},
url = {http://www.numdam.org/item/RSMUP_2003__110__147_0}
}

Castorina, Daniele; Mancini, Gianni. Non existence of bounded-energy solutions for some semilinear elliptic equations with a large parameter. Rendiconti del Seminario Matematico della Università di Padova, Volume 110 (2003) pp. 147-160. http://www.numdam.org/item/RSMUP_2003__110__147_0/`

[1] Adimurthi - G. Mancini, The Neumann problem for elliptic equations with critical non-linearity, A tribute in honor to G. Prodi, Scuola Normale Superiore di Pisa, 1991, pp. 9-25. | Zbl 0836.35048

[2] Adimurthi - G. Mancini - S. L. Yadava, The role of the mean curvature in semilinear Neumann problem involving critical exponent, Communications in Partial Differential Equations, 20 no. 3/4 (1995), pp. 591-631. | MR 1318082 | Zbl 0847.35047

[3] Adimurthi - F. Pacella - S. L. Yadava, Characterization of concentration points and LQ estimates for solutions of a semilinear Neumann problem involving the critical Sobolev exponent, Differential and Integral Equations, 8, no. 1 (1995), pp. 41-68. | MR 1296109 | Zbl 0814.35029

[4] D. Cao - E. S. Noussair - S. Yan, Existence and nonexistence of interior peaked solutions for a nonlinear Neumann problem, Pacific Journal of Mathematics, 200, no. 1 (2001), pp. 19-41. | MR 1863405 | Zbl 1140.35440

[5] P. Cherrier, Problems de Neumann nonlineaires sur les varietes riemanniennes, Journal of Functional Analysis, 57 (1984), pp. 154-206. | MR 749522 | Zbl 0552.58032

[6] O. Druet - E. Hebey - M. Vaugon, Pohozaev type obstructions and solutions of bounded energy for quasilinear elliptic equations with critical Sobolev growth. The conformally flat case, Nonlinear Anal., 51, no. 1 (2002), Ser A: Theory Methods, pp. 79-94. | MR 1915742 | Zbl 1066.35032

[7] V. Felli - E. Hebey - F. Robert, Fourth order equations of critical Sobolev growth. Energy function and solutions of bounded energy in the conformally flat case, preprint, June 2002. | MR 2184079 | Zbl 1086.58009

[8] N. Ghoussub - C. Gui - M. Zhu, On a singularly perturbed Neumann problem with the critical exponent, Comm. P.D.E., 6, no. 11-12 (2001), pp. 1929-1946. | MR 1876408 | Zbl 0997.35021

[9] D. Gilbarg - N. Trudinger, Elliptic Partial Differential Equations of Second Order, Springer, 1983. | MR 737190 | Zbl 0562.35001

[10] E. Hebey, Nonlinear elliptic equations of critical Sobolev growth from a dynamical point of view, preprint.

[11] G. Mancini - R. Musina, The role of the boundary in some semilinear Neumann problems, Rendiconti del Seminario Matematico della Università di Padova, 88 (1992), pp. 127-138. | Numdam | MR 1209119 | Zbl 0814.35037

[12] O. Rey, The question of interior blow-up points for an elliptic problem: the critical case, Journal de Mathematiques pures et appliquees, 81 (2002), pp. 655-696. | MR 1968337 | Zbl 1066.35033

[13] O. Rey, Boundary effect for an elliptic Neumann problem with critical nonlinearity, Communications in partial differential equations, 22, no. 7-8 (1997), pp. 1055-1139. | MR 1466311 | Zbl 0891.35040

[14] M. Struwe, Variational Methods, applications to nonlinear partial differential equations and Hamiltonian systems, Springer, 1990. | MR 1078018 | Zbl 0746.49010