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
 
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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
 
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