@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}, pages = {47--82}, publisher = {Gauthier-Villars}, volume = {17}, number = {1}, year = {2000}, zbl = {0944.35020}, mrnumber = {1743431}, language = {en}, url = {http://www.numdam.org/item/AIHPC_2000__17_1_47_0/} }

TY - JOUR AU - Gui, Changfeng AU - Wei, Juncheng AU - Winter, Matthias TI - Multiple boundary peak solutions for some singularly perturbed Neumann problems JO - Annales de l'I.H.P. Analyse non linéaire PY - 2000 DA - 2000/// SP - 47 EP - 82 VL - 17 IS - 1 PB - Gauthier-Villars UR - http://www.numdam.org/item/AIHPC_2000__17_1_47_0/ UR - https://zbmath.org/?q=an%3A0944.35020 UR - https://www.ams.org/mathscinet-getitem?mr=1743431 LA - en ID - AIHPC_2000__17_1_47_0 ER -

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, Volume 17 (2000) no. 1, pp. 47-82. http://www.numdam.org/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 | Zbl

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 | Zbl

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 | Zbl

and ,[4] Lectures on Elliptic Boundary Value Problems, Van Nostrand, Princeton, 1965. | MR | Zbl

,[5] Multidimensional nonlinear diffusion arising in population genetics, Adv. in Math. 30 (1978) 33-76. | MR | Zbl

and ,[6] A note on asymptotic uniqueness for some nonlinearities which change sign, Rocky Mountain Math. J. , to appear. | MR

,[7] Nonspreading wave packets for the cubic Schrödinger equation with a bounded potential, J. Funct. Anal. 69 (1986) 397-408. | MR | Zbl

and ,[8] The set of positive solutions of semilinear equations in large balls, Proc. Roy. Soc. Edinburgh 104 A (1986) 53-72. | MR | Zbl

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

, , and ,[10] Elliptic Partial Differential Equations of Second Order, 2nd ed., Springer, Berlin, 1983. | MR | Zbl

and ,[11] Multi-peak solutions for a semilinear Neumann problem, Duke Math. J. 84 (1996) 739-769. | MR | Zbl

,[12] Multi-peak solutions for a semilinear Neumann problem involving the critical Sobolev exponent, Math. Z. 229 (1998) 443-474. | MR | Zbl

and ,[13] Multiple interior peak solutions for some singularly perturbed Neumann problems, J. Differential Equations 158 (1999) 1-27. | MR | Zbl

and ,[14] Multiple wells in the semi-classical limit I, Comm. P.D.E. 9 (1984) 337-408. | MR | Zbl

and ,[15] On spike solutions of singularly perturbed semilinear Dirichlet problems, J. Differential Equations 114 (1994) 370-395. | MR | Zbl

,[16] Uniqueness of positive solutions of Δu - u + up = 0 in Rn, Arch. Rational Mech. Anal. 105 (1989) 243-266. | MR | Zbl

,[17] On a singularly perturbed equation with Neumann boundary condition, Comm. P.D.E. 23 (1998) 487-545. | MR | Zbl

,[18] Large amplitude stationary solutions to a chemotaxis systems, J. Differential Equations 72 (1988) 1-27. | MR | Zbl

, and ,[19] Non-Homogeneous Boundary Value Problems and Applications, Vol I, Springer, New York, Berlin, Heidelberg, Tokyo, 1972. | MR | Zbl

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 | Zbl

, and ,[21] On the shape of least energy solutions to a semilinear Neumann problem, Comm. Pure Appl. Math. 41 (1991) 819-851. | MR | Zbl

and ,[22] Locating the peaks of least energy solutions to a semilinear Neumann problem, Duke Math. J. 70 (1993) 247-281. | MR | Zbl

and ,[23] Point-condensation generated by a reaction-diffusion system in axially symmetric domains, Japan J. Industrial Appl. Math. 12 (1995) 327-365. | MR | Zbl

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 | Zbl

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 | Zbl

,[26] On positive multi-lump bound states of nonlinear Schrödinger equations under multiple-well potentials, Comm. Math. Phys. 131 (1990) 223-253. | MR | Zbl

,[27] Condensation of least-energy solutions of a semilinear Neumann problem, J. Partial Differential Equations 8 (1995) 1-36. | MR | Zbl

,[28] Condensation of least-energy solutions: the effect of boundary conditions, Nonlinear Analysis, TMA 24 (1995) 195-222. | MR | Zbl

,[29] Further study on the effect of boundary conditions, J. Differential Equations 117 (1995) 446-468. | MR | Zbl

,[30] Global bifurcation of steady-state solutions, J. Differential Equations 39 (1981) 269-290. | MR | Zbl

and ,[31] On the existence of multiple single-peaked solutions for a semilinear Neumann problem, Arch. Rational Mech. Anal. 120 (1992) 375-399. | MR | Zbl

,[32] An asymptotic analysis of localized solutions for some reaction-diffusion models in multidimensional domains, Stud. Appl. Math. 97 (1996) 103-126. | MR | Zbl

,[33] On the construction of single-peaked solutions of a singularly perturbed semilinear Dirichlet problem, J. Differential Equations 129 (1996) 315-333. | MR | Zbl

,[34] On the effect of the geometry of the domain in a singularly perturbed Dirichlet problem, Differential Integral Equations, to appear. | MR

,[35] On the boundary spike layer solutions of singularly perturbed semilinear Neumann problem, J. Differential Equations 134 (1997) 104-133. | MR | Zbl

,[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

,[37] Stationary solutions for the Cahn-Hilliard equation, Ann. Inst. H. Poincaré Anal. Non Linéaire 15 (1998) 459-492. | Numdam | MR | Zbl

and ,[38] Multiple boundary spike solutions for a wide class of singular perturbation problems, J. London Math. Soc. 59 (2) (1999) 585-606. | Zbl

and ,[39] Functional Analysis, 5th ed., Springer, Berlin, 1978. | MR | Zbl

,[40] Nonlinear Functional Analysis and its Applications I, Fixed-Point Theorems, Springer, Berlin, 1986. | MR | Zbl

,