Multiple interior peak solutions for some singularly perturbed neumann problems
Tóm tắt
Từ khóa
Tài liệu tham khảo
Agmon, 1965
Adimurthi, 1995, The role of mean curvature in a semilinear Neumann problem involving the critical Sobolev exponent, Comm. Partial Differential Equations, 20, 591, 10.1080/03605309508821110
Adimurthi, 1993, Interaction between the geometry of the boundary and positive solutions of a semilinear Neumann problem with critical nonlinearity, J. Funct. Anal., 31, 8
Adimurthi, 1995, Characterization of concentration points and L∞-estimates for solutions involving the critical Sobolev exponent, Differential Integral Equations, 8, 41, 10.57262/die/1369143783
Aronson, 1978, Multidimensional nonlinear diffusion arising in population genetics, Adv. Math., 30, 33, 10.1016/0001-8708(78)90130-5
P. Bates and G. Fusco, Equilibria with many nuclei for the Cahn-Hilliard equation, preprint.
Bahri, 1990, On a min-max procedure for the existence of a positive solution for certain scalar field equations in RN, Rev. Iberoamericana, 6, 1, 10.4171/RMI/92
Cao, 1996, On the existence and profile of multi-peaked solutions to singularly perturbed semilinear Dirichlet problem, Discrete Continuous Dynam. Systems, 2
M. Del Pino, P. Felmer, and J. Wei, Multiple-peak solutions for some singular perturbation problems, Cal. Var. Partial Differential Equations, in press.
Jang, 1994, On spike solutions of singularly perturbed semilinear Dirichlet problems, J. Differential Equations, 114, 370, 10.1006/jdeq.1994.1154
E.N. Dancer, A note on asymptotic uniqueness for some nonlinearities which change sign. Rocky Mountain Math. J., in press.
Fleming, 1986, Asymptotic series and the method of vanishing viscosity, Indiana Univ. Math. J., 35, 425, 10.1512/iumj.1986.35.35026
Floer, 1986, Nonspreading wave packets for the cubic Schrödinger equation with a bounded potential, J. Funct. Anal., 69, 397, 10.1016/0022-1236(86)90096-0
Gui, 1996, Multi-peak solutions for a semilinear Neumann problem, Duke Math. J., 84, 739, 10.1215/S0012-7094-96-08423-9
Gui, 1998, Multi-peak solutions for a semilinear Neumann problem invovling the critical Sobolev exponent, Math. Z., 229, 443, 10.1007/PL00004663
Gidas, 1981, Symmetry of positive solutions of nonlinear elliptic equations in RN, Vol. 7A, 369
Gardner, 1986, The set of positive solutions of semilinear equations in large balls, 104, 53
Gilbarg, 1983
Helffer, 1984, Multiple wells in the semi-classical limit, I, Comm. Partial Differential Equations, 9, 337, 10.1080/03605308408820335
M. Kowalczyk, Multiple spike layers in the shadow Gierer-Meihardt system: Existence of equilibria and approximate invariant manifold, preprint.
Kwong, 1989, Uniqueness of positive solutions of Δu −u + up = 0 in Rn, Arch. Rational Mech. Anal., 105, 243, 10.1007/BF00251502
Lin, 1988, Large amplitude stationary solutions to a chemotaxis systems, J. Differential Equations, 72, 1, 10.1016/0022-0396(88)90147-7
Lions, 1972, Vol. I
Li, 1998, On a singularly perturbed equation with Neumann boundary condition, Comm. Partial Differential Equations, 23, 487, 10.1080/03605309808821354
Ni, 1992, Singular behavior of least-energy solutions of a semi-linear Neumann problem involving critical Sobolev exponents, Duke Math. J., 67, 1, 10.1215/S0012-7094-92-06701-9
Ni, 1991, On the shape of least energy solution to a semilinear Neumann problem, Comm. Pure Appl. Math., 41, 819, 10.1002/cpa.3160440705
Ni, 1993, Locating the peaks of least energy solutions to a semilinear Neumann problem, Duke Math. J., 70, 247, 10.1215/S0012-7094-93-07004-4
Ni, 1995, Point-condensation generated be a reaction-diffusion system in axially symmetric domains, Japan J. Indust. Appl. Math., 12, 327, 10.1007/BF03167294
Ni, 1995, On the location and profile of spike-layer solutions to singularly perturbed semilinear Dirichlet problems, Comm. Pure Appl. Math., 48, 731, 10.1002/cpa.3160480704
Oh, 1988, Existence of semi-classical bound states of nonlinear Schrödinger equations with potentials of the class (V)a, Comm. Partial Differential Equations, 13, 1499, 10.1080/03605308808820585
Oh, 1990, On positive multi-lump bound states of nonlinear Schrödinger equations under multiple-well potentials, Comm. Math. Phys., 131, 223, 10.1007/BF02161413
Pan, 1995, Condensation of least-energy solutions of a semilinear Neumann problem, J. Partial Differential Equations, 8, 1
Pan, 1995, Condensation of least-energy solutions: The effect of boundary conditions, Nonlinear Anal., 24, 195, 10.1016/0362-546X(94)E0056-M
Pan, 1995, Further study on the effect of boundary conditions, J. Differential Equations, 117, 446, 10.1006/jdeq.1995.1061
Smoller, 1981, Global bifurcation of steady-state solutions, J. Differential Equations, 39, 269, 10.1016/0022-0396(81)90077-2
Wang, 1992, On the existence of multiple single-peaked solutions for a semilinear Neumann problem, Arch. Rational Mech. Anal., 120, 375, 10.1007/BF00380322
Ward, 1996, An asymptotic analysis of localized solutions for some reaction-diffusion models in multidimensional domains, Stud. Appl. Math., 97, 103, 10.1002/sapm1996972103
Wei, 1996, On the construction of single-peaked solutions of a singularly perturbed semilinear Dirichlet problem, J. Differential Equations, 129, 315, 10.1006/jdeq.1996.0120
J. Wei, On the effect of the geometry of the domain in a singularly perturbed Dirichlet problem, Differential Integral Equations, in press.
Wei, 1998, On the interior spike layer solutions of a singularly perturbed Neumann problem, Tohôku Math. J., 50, 159, 10.2748/tmj/1178224971
Wei, 1997, On the boundary spike layer solutions of singularly perturbed semilinear Neumann problem, J. Differential Equations, 134, 10.1006/jdeq.1996.3218
J. Wei, On the construction of single interior peak solutions for a singularly perturbed Neumann problem, submitted for publication.
Wei, 1998, Stationary solutions for the Cahn-Hilliard equation, Ann. Inst. H. Poincaré Anal. Non Linéaire, 15, 459, 10.1016/S0294-1449(98)80031-0
J. Wei and M. Winter, Multiple boundary spike solutions for a wide class of singular perturbation problems, J. London Math. Soc., in press.
Yosida, 1978
Zeidler, 1986