Non existence of bounded-energy solutions for some semilinear elliptic equations with a large parameter

Daniele Castorina; Gianni Mancini

Rendiconti del Seminario Matematico della Università di Padova (2003)

  • Volume: 110, page 147-160
  • ISSN: 0041-8994

How to cite

top

Castorina, Daniele, and 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 110 (2003): 147-160. <http://eudml.org/doc/108611>.

@article{Castorina2003,
author = {Castorina, Daniele, Mancini, Gianni},
journal = {Rendiconti del Seminario Matematico della Università di Padova},
language = {eng},
pages = {147-160},
publisher = {Seminario Matematico of the University of Padua},
title = {Non existence of bounded-energy solutions for some semilinear elliptic equations with a large parameter},
url = {http://eudml.org/doc/108611},
volume = {110},
year = {2003},
}

TY - JOUR
AU - Castorina, Daniele
AU - Mancini, Gianni
TI - Non existence of bounded-energy solutions for some semilinear elliptic equations with a large parameter
JO - Rendiconti del Seminario Matematico della Università di Padova
PY - 2003
PB - Seminario Matematico of the University of Padua
VL - 110
SP - 147
EP - 160
LA - eng
UR - http://eudml.org/doc/108611
ER -

References

top
  1. [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. Zbl0836.35048
  2. [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. Zbl0847.35047MR1318082
  3. [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. Zbl0814.35029MR1296109
  4. [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. Zbl1140.35440MR1863405
  5. [5] P. CHERRIER, Problems de Neumann nonlineaires sur les varietes riemanniennes, Journal of Functional Analysis, 57 (1984), pp. 154-206. Zbl0552.58032MR749522
  6. [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. Zbl1066.35032MR1915742
  7. [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. Zbl1086.58009MR2184079
  8. [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. Zbl0997.35021MR1876408
  9. [9] D. GILBARG - N. TRUDINGER, Elliptic Partial Differential Equations of Second Order, Springer, 1983. Zbl0562.35001MR737190
  10. [10] E. HEBEY, Nonlinear elliptic equations of critical Sobolev growth from a dynamical point of view, preprint. Zbl1210.35092
  11. [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. Zbl0814.35037MR1209119
  12. [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. Zbl1066.35033MR1968337
  13. [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. Zbl0891.35040MR1466311
  14. [14] M. STRUWE, Variational Methods, applications to nonlinear partial differential equations and Hamiltonian systems, Springer, 1990. Zbl0746.49010MR1078018

NotesEmbed ?

top

You must be logged in to post comments.

To embed these notes on your page include the following JavaScript code on your page where you want the notes to appear.

Only the controls for the widget will be shown in your chosen language. Notes will be shown in their authored language.

Tells the widget how many notes to show per page. You can cycle through additional notes using the next and previous controls.

    
                

Note: Best practice suggests putting the JavaScript code just before the closing </body> tag.