@article{AIHPC_2005__22_4_459_0, author = {Rey, Olivier and Wei, Juncheng}, title = {Blowing up solutions for an elliptic {Neumann} problem with sub- or supercritical nonlinearity. {Part} {II} : $N\ge 4$}, journal = {Annales de l'I.H.P. Analyse non lin\'eaire}, pages = {459--484}, publisher = {Elsevier}, volume = {22}, number = {4}, year = {2005}, doi = {10.1016/j.anihpc.2004.07.004}, mrnumber = {2145724}, zbl = {02191850}, language = {en}, url = {http://archive.numdam.org/articles/10.1016/j.anihpc.2004.07.004/} }
TY - JOUR AU - Rey, Olivier AU - Wei, Juncheng TI - Blowing up solutions for an elliptic Neumann problem with sub- or supercritical nonlinearity. Part II : $N\ge 4$ JO - Annales de l'I.H.P. Analyse non linéaire PY - 2005 SP - 459 EP - 484 VL - 22 IS - 4 PB - Elsevier UR - http://archive.numdam.org/articles/10.1016/j.anihpc.2004.07.004/ DO - 10.1016/j.anihpc.2004.07.004 LA - en ID - AIHPC_2005__22_4_459_0 ER -
%0 Journal Article %A Rey, Olivier %A Wei, Juncheng %T Blowing up solutions for an elliptic Neumann problem with sub- or supercritical nonlinearity. Part II : $N\ge 4$ %J Annales de l'I.H.P. Analyse non linéaire %D 2005 %P 459-484 %V 22 %N 4 %I Elsevier %U http://archive.numdam.org/articles/10.1016/j.anihpc.2004.07.004/ %R 10.1016/j.anihpc.2004.07.004 %G en %F AIHPC_2005__22_4_459_0
Rey, Olivier; Wei, Juncheng. Blowing up solutions for an elliptic Neumann problem with sub- or supercritical nonlinearity. Part II : $N\ge 4$. Annales de l'I.H.P. Analyse non linéaire, Volume 22 (2005) no. 4, pp. 459-484. doi : 10.1016/j.anihpc.2004.07.004. http://archive.numdam.org/articles/10.1016/j.anihpc.2004.07.004/
[1] The Neumann problem for elliptic equations with critical nonlinearity, “A tribute in honour of G. Prodi”, Scuola Norm. Sup. Pisa (1991) 9-25. | Zbl
, ,[2] Geometry and topology of the boundary in the critical Neumann problem, J. Reine Angew. Math. 456 (1994) 1-18. | EuDML | MR | Zbl
, ,[3] 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. | MR | Zbl
, , ,[4] Critical Points at Infinity in Some Variational Problems, Pitman Res. Notes Math. Ser., vol. 182, Longman, 1989. | MR | Zbl
,[5] Equilibria with many nuclei for the Cahn-Hilliard equation, J. Differential Equations 160 (2000) 283-356. | MR | Zbl
, ,[6] Asymptotic symmetry and local behavior of semilinear elliptic equations with critical Sobolev growth, Comm. Pure Appl. Math. 42 (1989) 271-297. | MR | Zbl
, , ,[7] Multiplicity of multiple interior peaks solutions for some singularly perturbed Neumann problems, Intern. Math. Res. Notes 12 (1998) 601-626. | MR | Zbl
, ,[8] Multipeak solutions for a singularly perturbed Neumann problem, Pacific J. Math. 189 (1999) 241-262. | MR | Zbl
, ,[9] Two-bubble solutions in the super-critical Bahri-Coron's problem, Calc. Var. Partial Differential Equations 16 (2003) 113-145. | MR | Zbl
, , ,[10] On the effect of critical points of distance function in superlinear elliptic problems, Adv. Differential Equations 5 (2000) 1397-1420. | MR | Zbl
, ,[11] Existence of multipeak solutions for a semilinear elliptic problem via nonsmooth critical point theory, Calc. Var. Partial Differential Equations 11 (2000) 143-175. | MR | Zbl
, , ,[12] A theory of biological pattern formation, Kybernetik (Berlin) 12 (1972) 30-39.
, ,[13] Multi-peak solutions for a semilinear Neumann problem, Duke Math. J. 84 (1996) 739-769. | MR | Zbl
,[14] Estimates for boundary-bubbling solutions to an elliptic Neumann problem, J. Reine Angew. Math. 546 (2002) 201-235. | MR | Zbl
, ,[15] Multiple interior peak solutions for some singularly perturbed Neumann problems, J. Differential Equations 158 (1999) 1-27. | MR | Zbl
, ,[16] C. Gui, J. Wei, On the existence of arbitrary number of bubbles for some semilinear elliptic equations with critical Sobolev exponent, in press.
[17] On multiple mixed interior and boundary peak solutions for some singularly perturbed Neumann problems, Canad. J. Math. 52 (2000) 522-538. | MR | Zbl
, ,[18] Multiple boundary peak solutions for some singularly perturbed Neumann problems, Ann. Inst. H. Poincaré Anal. Non Linéaire 17 (2000) 47-82. | Numdam | MR | Zbl
, , ,[19] A criterion for existence of solutions to the supercritical Bahri-Coron's problem, Houston J. Math. 30 (2004) 587-613. | MR | Zbl
, ,[20] Multiple spike layers in the shadow Gierer-Meinhardt system: existence of equilibria and quasi-invariant manifold, Duke Math. J. 98 (1999) 59-111. | MR | Zbl
,[21] On conformal scalar curvature equation in , Duke Math. J. 57 (1988) 895-924. | MR | Zbl
, ,[22] On a singularly perturbed equation with Neumann boundary condition, Comm. Partial Differential Equations 23 (1998) 487-545. | MR | Zbl
,[23] On the Diffusion Coefficient of a Semilinear Neumann Problem, Lecture Notes in Math., vol. 1340, Springer, New York, 1986. | MR | Zbl
, ,[24] Large amplitude stationary solutions to a chemotaxis system, J. Differential Equations 72 (1988) 1-27. | MR | Zbl
, , ,[25] The behavior of the Laplacian on weighted Sobolev spaces, Comm. Pure Appl. Math. 32 (1979) 783-795. | MR | Zbl
,[26] On Neumann problems for semilinear elliptic equations with critical nonlinearity: existence and symmetry of multi-peaked solutions, Comm. Partial Differential Equations 22 (1997) 1493-1527. | MR | Zbl
, , ,[27] Diffusion, cross-diffusion, and their spike-layer steady states, Notices Amer. Math. Soc. 45 (1998) 9-18. | MR | Zbl
,[28] Singular behavior of least-energy solutions of a semi-linear Neumann problem involving critical Sobolev exponents, Duke Math. J. 67 (1992) 1-20. | MR | Zbl
, , ,[29] On the shape of least-energy solutions to a semi-linear problem Neumann problem, Comm. Pure Appl. Math. 44 (1991) 819-851. | MR | Zbl
, ,[30] Locating the peaks of least-energy solutions to a semi-linear Neumann problem, Duke Math. J. 70 (1993) 247-281. | MR | Zbl
, ,[31] The role of the Green's function in a nonlinear elliptic problem involving the critical Sobolev exponent, J. Funct. Anal. 89 (1990) 1-52. | MR | Zbl
,[32] An elliptic Neumann problem with critical nonlinearity in three dimensional domains, Comm. Contemp. Math. 1 (1999) 405-449. | MR | Zbl
,[33] The question of interior blow-up points for an elliptic Neumann problem: the critical case, J. Math. Pures Appl. 81 (2002) 655-696. | MR | Zbl
,[34] O. Rey, J. Wei, Blow-up solutions for an elliptic Neumann problem with sub- or supercritical nonlinearity, I: , J. Funct. Anal., in press. | Zbl
[35] Neumann problem of semilinear elliptic equations involving critical Sobolev exponents, J. Differential Equations 93 (1991) 283-310. | MR | Zbl
,[36] The effect of domain geometry on the number of positive solutions of Neumann problems with critical exponents, Differential Integral Equations 8 (1995) 1533-1554. | MR | Zbl
,[37] High energy and multi-peaked solutions for a nonlinear Neumann problem with critical exponent, Proc. Roy. Soc. Edinburgh Sect. A 125 (1995) 1003-1029. | MR | Zbl
,[38] Construction of multi-peaked solution for a nonlinear Neumann problem with critical exponent, J. Nonlinear Anal. 27 (1996) 1281-1306. | MR | Zbl
,[39] On the equation in , Rend. Circ. Mat. Palermo 2 (1995) 365-400. | Zbl
, ,[40] On the interior spike layer solutions of singularly perturbed semilinear Neumann problems, Tohoku Math. J. 50 (1998) 159-178. | MR | Zbl
,[41] J. Wei, X. Xu, Uniqueness and a priori estimates for some nonlinear elliptic Neumann equations in , Pacific J. Math., in press. | MR | Zbl
[42] Stationary solutions for the Cahn-Hilliard equation, Ann. Inst. H. Poincaré, Anal. Non Linéaire 15 (1998) 459-482. | Numdam | MR | Zbl
, ,[43] On the number of interior multipeak solutions for singularly perturbed Neumann problems, Topol. Methods Nonlinear Anal. 12 (1998) 61-78. | MR | Zbl
,[44] Uniqueness results through a priori estimates, I. A three dimensional Neumann problem, J. Differential Equations 154 (1999) 284-317. | MR | Zbl
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