Super-critical boundary bubbling in a semilinear Neumann problem
Manuel del Pino; Monica Musso; Angela Pistoia
Annales de l'I.H.P. Analyse non linéaire (2005)
- Volume: 22, Issue: 1, page 45-82
- ISSN: 0294-1449
Access Full Article
topHow to cite
topdel Pino, Manuel, Musso, Monica, and Pistoia, Angela. "Super-critical boundary bubbling in a semilinear Neumann problem." Annales de l'I.H.P. Analyse non linéaire 22.1 (2005): 45-82. <http://eudml.org/doc/78647>.
@article{delPino2005,
author = {del Pino, Manuel, Musso, Monica, Pistoia, Angela},
journal = {Annales de l'I.H.P. Analyse non linéaire},
keywords = {critical Sobolev exponent; Neumann boundary conditions; mean curvature; bubble solutions; Lyapunov-Schmidt reduction},
language = {eng},
number = {1},
pages = {45-82},
publisher = {Elsevier},
title = {Super-critical boundary bubbling in a semilinear Neumann problem},
url = {http://eudml.org/doc/78647},
volume = {22},
year = {2005},
}
TY - JOUR
AU - del Pino, Manuel
AU - Musso, Monica
AU - Pistoia, Angela
TI - Super-critical boundary bubbling in a semilinear Neumann problem
JO - Annales de l'I.H.P. Analyse non linéaire
PY - 2005
PB - Elsevier
VL - 22
IS - 1
SP - 45
EP - 82
LA - eng
KW - critical Sobolev exponent; Neumann boundary conditions; mean curvature; bubble solutions; Lyapunov-Schmidt reduction
UR - http://eudml.org/doc/78647
ER -
References
top- [1] Adimurthi, Mancini G., The Neumann problem for elliptic equations with critical nonlinearity, A tribute in honour of G. Prodi, Scuola Norm. Sup. Pisa (1991) 9-25. Zbl0836.35048MR1205370
- [2] Adimurthi, Mancini G., Geometry and topology of the boundary in the critical Neumann problem, J. Reine Angew. Math.456 (1994) 1-18. Zbl0804.35036MR1301449
- [3] Adimurthi, Mancini G., Yadava S.L., The role of the mean curvature in semilinear Neumann problem involving critical exponent, Comm. Partial Differential Equations20 (3–4) (1995) 591-631. Zbl0847.35047MR1318082
- [4] Adimurthi, Pacella F., Yadava S.L., Interaction between the geometry of the boundary and positive solutions of a semilinear Neumann problem with critical nonlinearity, J. Funct. Anal.113 (1993) 318-350. Zbl0793.35033MR1218099
- [5] Adimurthi, Pacella F., Yadava S.L., Characterization of concentration points and -estimates for solutions of a semilinear Neumann problem involving the critical Sobolev exponent, Differential Integral Equations8 (1) (1995) 41-68. Zbl0814.35029MR1296109
- [6] Cao D., Noussair E.S., The effect of geometry of the domain boundary in an elliptic Neumann problem, Adv. Differential Equations6 (8) (2001) 931-958. Zbl1140.35411MR1828499
- [7] Dancer E.N., Yan S., Multipeak solutions for a singularly perturbed Neumann problem, Pacific J. Math.189 (2) (1999) 241-262. Zbl0933.35070MR1696122
- [8] del Pino M., Dolbeault J., Musso M., “Bubble-tower” radial solutions in the slightly supercritical Brezis–Nirenberg problem, J. Differential Equations193 (2) (2003) 280-306. Zbl1140.35413
- [9] del Pino M., Felmer P., Spike-layered solutions of singularly perturbed elliptic problems in a degenerate setting, Indiana Univ. Math. J.48 (3) (1999) 883-898. Zbl0932.35080MR1736974
- [10] del Pino M., Felmer P., Musso M., Two-bubble solutions in the super-critical Bahri–Coron's problem, Calc. Var. PDE16 (2) (2003) 113-145. Zbl1142.35421MR1956850
- [11] del Pino M., Felmer P., Wei J., On the role of mean curvature in some singularly perturbed Neumann problems, SIAM J. Math. Anal.31 (1) (1999) 63-79. Zbl0942.35058MR1742305
- [12] Fowler R.H., Further studies on Emden's and similar differential equations, Quart. J. Math.2 (1931) 259-288. Zbl0003.23502
- [13] Grossi M., A class of solutions for the Neumann problem , Duke Math. J.79 (2) (1995) 309-334. Zbl1043.35507MR1344764
- [14] Grossi M., Pistoia A., Wei J., Existence of multipeak solutions for a semilinear Neumann problem via nonsmooth critical point theory, Calc. Var. Partial Differential Equations11 (2) (2000) 143-175. Zbl0964.35047MR1782991
- [15] Gui C., Multi-peak solutions for a semilinear Neumann problem, Duke Math. J.84 (1996) 739-769. Zbl0866.35039MR1408543
- [16] Gui C., Ghoussoub N., Multi-peak solutions for a semilinear Neumann problem involving the critical Sobolev exponent, Math. Z.229 (3) (1998) 443-474. Zbl0955.35024MR1658569
- [17] Gui C., Lin C.-S., Estimates for boundary-bubbling solutions to an elliptic Neumann problem, J. Reine Angew. Math.546 (2002) 201-235. Zbl1136.35380MR1900999
- [18] Gui C., Wei J., Multiple interior peak solutions for some singularly perturbed Neumann problems, J. Differential Equations158 (1) (1999) 1-27. Zbl1061.35502MR1721719
- [19] Kowalczyk M., Multiple spike layers in the shadow Gierer–Meinhardt system: existence of equilibria and the quasi-invariant manifold, Duke Math. J.98 (1) (1999) 59-111. Zbl0962.35063MR1687412
- [20] Li Y.Y., On a singularly perturbed equation with Neumann boundary condition, Comm. Partial Differential Equations23 (3–4) (1998) 487-545. Zbl0898.35004MR1620632
- [21] Li Y.Y., Prescribing scalar curvature on and related problems, part I, J. Differential Equations120 (1996) 541-597. Zbl0849.53031MR1383201
- [22] Y.Y. Li, L. Zhang, Liouville and Harnack type theorems for semilinear elliptic equations, preprint. Zbl1173.35477
- [23] Lin C.-S., Locating the peaks of solutions via the maximum principle, I. The Neumann problem, Comm. Pure Appl. Math.54 (2001) 1065-1095. Zbl1035.35039MR1835382
- [24] Lin C.-S., Ni W.-M., Takagi I., Large amplitude stationary solutions to a chemotaxis system, J. Differential Equations72 (1988) 1-27. Zbl0676.35030MR929196
- [25] Ni W.-M., Takagi I., On the shape of least-energy solutions to a semilinear Neumann problem, Comm. Pure Appl. Math.44 (1991) 819-851. Zbl0754.35042MR1115095
- [26] Ni W.-M., Takagi I., Locating the peaks of least-energy solutions to a semilinear Neumann problem, Duke Math. J70 (1993) 247-281. Zbl0796.35056MR1219814
- [27] Ni W.-M., B Pan X., Takagi I., Singular behavior of least-energy solutions of a semilinear Neumann problem involving critical Sobolev exponents, Duke Math. J.67 (1) (1992) 1-20. Zbl0785.35041MR1174600
- [28] Rey O., The role of the Green's function in a nonlinear elliptic equation involving the critical Sobolev exponent, J. Funct. Anal.89 (1) (1990) 1-52. Zbl0786.35059MR1040954
- [29] Rey O., Boundary effect for an elliptic Neumann problem with critical nonlinearity, Comm. in PDE22 (1997) 1055-1139. Zbl0891.35040MR1466311
- [30] Rey O., An elliptic Neumann problem with critical nonlinearity in three dimensional domains, Comm. Contemp. Math.1 (1999) 405-449. Zbl0954.35065MR1707889
- [31] O. Rey, J. Wei, Blowing up solutions for an elliptic Neumann problem with sub- or supercritical nonlinearity, part I: , J. Funct. Anal., submitted for publication. Zbl1134.35049
- [32] Wang X.J., Neumann problem of semilinear elliptic equations involving critical Sobolev exponent, J. Differential Equations93 (1991) 283-301. Zbl1068.34060MR1125221
- [33] Wang Z.Q., The effect of domain geometry on the number of positive solutions of Neumann problems with critical exponents, Differential Integral Equations8 (1995) 1533-1554. Zbl0829.35041MR1329855
- [34] Wei J., On the boundary spike layer solutions to a singularly perturbed Neumann problem, J. Differential Equations134 (1) (1997) 104-133. Zbl0873.35007MR1429093
Citations in EuDML Documents
topNotesEmbed ?
topTo embed these notes on your page include the following JavaScript code on your page where you want the notes to appear.