@article{AIHPC_2000__17_1_47_0, author = {Gui, Changfeng and Wei, Juncheng and Winter, Matthias}, title = {Multiple boundary peak solutions for some singularly perturbed Neumann problems}, journal = {Annales de l'I.H.P. Analyse non lin\'eaire}, volume = {17}, year = {2000}, pages = {47-82}, mrnumber = {1743431}, zbl = {0944.35020}, language = {en}, url = {http://dml.mathdoc.fr/item/AIHPC_2000__17_1_47_0} }
Gui, Changfeng; Wei, Juncheng; Winter, Matthias. Multiple boundary peak solutions for some singularly perturbed Neumann problems. Annales de l'I.H.P. Analyse non linéaire, Tome 17 (2000) pp. 47-82. http://gdmltest.u-ga.fr/item/AIHPC_2000__17_1_47_0/
[1] The role of mean curvature in a semilinear Neumann problem involving the critical Sobolev exponent, Comm. P.D.E. 20 (1995) 591-631. | MR 1318082 | Zbl 0847.35047
and ,[2] 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 1218099 | Zbl 0793.35033
and ,[3] Characterization of concentration points and L∞-estimates for solutions involving the critical Sobolev exponent, Differential Integral Equations 8 (1) (1995) 41-68. | MR 1296109 | Zbl 0814.35029
and ,[4] Lectures on Elliptic Boundary Value Problems, Van Nostrand, Princeton, 1965. | MR 178246 | Zbl 0142.37401
,[5] Multidimensional nonlinear diffusion arising in population genetics, Adv. in Math. 30 (1978) 33-76. | MR 511740 | Zbl 0407.92014
and ,[6] A note on asymptotic uniqueness for some nonlinearities which change sign, Rocky Mountain Math. J. , to appear. | MR 1748710
,[7] Nonspreading wave packets for the cubic Schrödinger equation with a bounded potential, J. Funct. Anal. 69 (1986) 397-408. | MR 867665 | Zbl 0613.35076
and ,[8] The set of positive solutions of semilinear equations in large balls, Proc. Roy. Soc. Edinburgh 104 A (1986) 53-72. | MR 877892 | Zbl 0625.35030
and ,[9] Symmetry of positive solutions of nonlinear elliptic equations in Rn, in: Mathematical Analysis and Applications, Part A, Adv. Math. Suppl. Studies, Vol. 7A, Academic Press, New York, 1981, pp. 369-402. | Zbl 0469.35052
, , and ,[10] Elliptic Partial Differential Equations of Second Order, 2nd ed., Springer, Berlin, 1983. | MR 737190 | Zbl 0562.35001
and ,[11] Multi-peak solutions for a semilinear Neumann problem, Duke Math. J. 84 (1996) 739-769. | MR 1408543 | Zbl 0866.35039
,[12] Multi-peak solutions for a semilinear Neumann problem involving the critical Sobolev exponent, Math. Z. 229 (1998) 443-474. | MR 1658569 | Zbl 0955.35024
and ,[13] Multiple interior peak solutions for some singularly perturbed Neumann problems, J. Differential Equations 158 (1999) 1-27. | MR 1721719 | Zbl 1061.35502
and ,[14] Multiple wells in the semi-classical limit I, Comm. P.D.E. 9 (1984) 337-408. | MR 740094 | Zbl 0546.35053
and ,[15] On spike solutions of singularly perturbed semilinear Dirichlet problems, J. Differential Equations 114 (1994) 370-395. | MR 1303033 | Zbl 0812.35008
,[16] Uniqueness of positive solutions of Δu - u + up = 0 in Rn, Arch. Rational Mech. Anal. 105 (1989) 243-266. | MR 969899 | Zbl 0676.35032
,[17] On a singularly perturbed equation with Neumann boundary condition, Comm. P.D.E. 23 (1998) 487-545. | MR 1620632 | Zbl 0898.35004
,[18] Large amplitude stationary solutions to a chemotaxis systems, J. Differential Equations 72 (1988) 1-27. | MR 929196 | Zbl 0676.35030
, and ,[19] Non-Homogeneous Boundary Value Problems and Applications, Vol I, Springer, New York, Berlin, Heidelberg, Tokyo, 1972. | MR 350177 | Zbl 0223.35039
and ,[20] Singular behavior of least-energy solutions of a semilinear Neumann problem involving critical Sobolev exponents, Duke Math. J. 67 (1992) 1-20. | MR 1174600 | Zbl 0785.35041
, and ,[21] On the shape of least energy solutions to a semilinear Neumann problem, Comm. Pure Appl. Math. 41 (1991) 819-851. | MR 1115095 | Zbl 0754.35042
and ,[22] Locating the peaks of least energy solutions to a semilinear Neumann problem, Duke Math. J. 70 (1993) 247-281. | MR 1219814 | Zbl 0796.35056
and ,[23] Point-condensation generated by a reaction-diffusion system in axially symmetric domains, Japan J. Industrial Appl. Math. 12 (1995) 327-365. | MR 1337211 | Zbl 0843.35006
and ,[24] On the location and profile of spike-layer solutions to singularly perturbed semilinear Dirichlet problems, Comm. Pure Appl. Math. 48 (1995) 731-768. | MR 1342381 | Zbl 0838.35009
and ,[25] Existence of semi-classical bound states of nonlinear Schrödinger equations with potentials of the class (V)a, Comm. P.D.E. 13 (12) (1988) 1499- 1519. | MR 970154 | Zbl 0702.35228
,[26] On positive multi-lump bound states of nonlinear Schrödinger equations under multiple-well potentials, Comm. Math. Phys. 131 (1990) 223-253. | MR 1065671 | Zbl 0753.35097
,[27] Condensation of least-energy solutions of a semilinear Neumann problem, J. Partial Differential Equations 8 (1995) 1-36. | MR 1317288 | Zbl 0814.35039
,[28] Condensation of least-energy solutions: the effect of boundary conditions, Nonlinear Analysis, TMA 24 (1995) 195-222. | MR 1312590 | Zbl 0826.35037
,[29] Further study on the effect of boundary conditions, J. Differential Equations 117 (1995) 446-468. | MR 1325806 | Zbl 0832.35050
,[30] Global bifurcation of steady-state solutions, J. Differential Equations 39 (1981) 269-290. | MR 607786 | Zbl 0425.34028
and ,[31] On the existence of multiple single-peaked solutions for a semilinear Neumann problem, Arch. Rational Mech. Anal. 120 (1992) 375-399. | MR 1185568 | Zbl 0784.35035
,[32] An asymptotic analysis of localized solutions for some reaction-diffusion models in multidimensional domains, Stud. Appl. Math. 97 (1996) 103-126. | MR 1395845 | Zbl 0932.35059
,[33] On the construction of single-peaked solutions of a singularly perturbed semilinear Dirichlet problem, J. Differential Equations 129 (1996) 315-333. | MR 1404386 | Zbl 0865.35011
,[34] On the effect of the geometry of the domain in a singularly perturbed Dirichlet problem, Differential Integral Equations, to appear. | MR 1811947
,[35] On the boundary spike layer solutions of singularly perturbed semilinear Neumann problem, J. Differential Equations 134 (1997) 104-133. | MR 1429093 | Zbl 0873.35007
,[36] On the construction of single interior peak solutions for a singularly perturbed Neumann problem, in: Partial Differential Equations: Theory and Numerical solution; CRC Press LLC, 1998, pp. 336-349. | Zbl 0931.35018
,[37] Stationary solutions for the Cahn-Hilliard equation, Ann. Inst. H. Poincaré Anal. Non Linéaire 15 (1998) 459-492. | Numdam | MR 1632937 | Zbl 0910.35049
and ,[38] Multiple boundary spike solutions for a wide class of singular perturbation problems, J. London Math. Soc. 59 (2) (1999) 585-606. | Zbl 0922.35025
and ,[39] Functional Analysis, 5th ed., Springer, Berlin, 1978. | MR 500055 | Zbl 0365.46001
,[40] Nonlinear Functional Analysis and its Applications I, Fixed-Point Theorems, Springer, Berlin, 1986. | MR 816732 | Zbl 0583.47050
,