@article{AIHPC_2003__20_1_107_0, author = {Nakashima, Kimie and Tanaka, Kazunaga}, title = {Clustering layers and boundary layers in spatially inhomogeneous phase transition problems}, journal = {Annales de l'I.H.P. Analyse non lin\'eaire}, volume = {20}, year = {2003}, pages = {107-143}, mrnumber = {1958164}, zbl = {01901029}, language = {en}, url = {http://dml.mathdoc.fr/item/AIHPC_2003__20_1_107_0} }
Nakashima, Kimie; Tanaka, Kazunaga. Clustering layers and boundary layers in spatially inhomogeneous phase transition problems. Annales de l'I.H.P. Analyse non linéaire, Tome 20 (2003) pp. 107-143. http://gdmltest.u-ga.fr/item/AIHPC_2003__20_1_107_0/
[1] S. Ai, S.P. Hastings, A shooting approach to layers and chaos in a forced duffing equation, I, Preprint. | MR 1935609
[2] Semiclassical states of nonlinear Schrödinger equations, Arch. Rat. Mech. Anal. 140 (1997) 285-300. | MR 1486895 | Zbl 0896.35042
, , ,[3] Stable transition layers in a semilinear boundary value problem, J. Differential Equations 67 (1987) 212-242. | MR 879694 | Zbl 0634.35041
, , ,[4] Multiple solutions for a class of nonlinear Sturm-Liouville problems on the half line, J. Differential Equations 85 (1990) 236-275. | MR 1054550 | Zbl 0703.34032
,[5] Local mountain passes for semilinear elliptic problems in unbounded domains, Calc. Var. PDE 4 (1996) 121-137. | MR 1379196 | Zbl 0844.35032
, ,[6] Multi-peak bound states of nonlinear Schrödinger equations, Ann. IHP, Analyse Nonlinéaire 15 (1998) 127-149. | Numdam | MR 1614646 | Zbl 0901.35023
, ,[7] Nonspreading wave packets for the cubic Schrödinger equation with a bounded potential, J. Funct. Anal. 69 (3) (1986) 397-408. | MR 867665 | Zbl 0613.35076
, ,[8] Chaotic solutions in slowly varying perturbations of Hamiltonian systems with applications to shallow water sloshing, J. Dynam. Differential Equations 14 (2002) 63-84. | MR 1878245 | Zbl 1005.37028
, , , ,[9] Existence of multi-bump solutions for nonlinear Schrödinger equations via variational method, Comm. Partial Differential Equations 21 (1996) 787-820. | MR 1391524 | Zbl 0857.35116
,[10] Multiple interior peak solutions for some singularly perturbed Neumann problems, J. Differential Equations 158 (1999) 1-27. | MR 1721719 | Zbl 1061.35502
, ,[11] Multiple solutions for a class of nonlinear boundary value problems, Indiana Univ. Math. J. 20 (11) (1971) 983-996. | MR 279423 | Zbl 0225.35045
,[12] On interacting bumps of semi-classical states of nonlinear Schrödinger equations, Adv. Differential Equations 5 (2000) 899-928. | MR 1776345 | Zbl 01700753
, ,[13] Slowly varying phase planes and boundary-layer theory, Stud. Appl. Math. 72 (3) (1985) 221-239. | MR 790130 | Zbl 0586.76047
,[14] On a singularly perturbed elliptic equation, Adv. Differential Equations 2 (1997) 955-980. | MR 1606351 | Zbl 1023.35500
,[15] K. Nakashima, Multi-layered stationary solutions for a spatially inhomogeneous Allen-Cahn equation, J. Differential Equations, to appear. | MR 1973289 | Zbl 1034.34024
[16] Stable transition layers in a balanced bistable equation, Differential Integral Equations 13 (2000) 1025-1038. | MR 1775244 | Zbl 0981.34011
,[17] Existence of semiclassical bound states of nonlinear Schrödinger equations with potentials of the class (V)a, Comm. Partial Differential Equations 13 (1988) 1499-1519. | MR 970154 | Zbl 0702.35228
,[18] Stability of semiclassical bound states of nonlinear Schrödinger equations with potentials, Comm. Math. Phys. 121 (1989) 11-33. | MR 985612 | Zbl 0693.35132
,[19] On positive multi-lump bound states of nonlinear Schrödinger equations under multiple well potential, Comm. Math. Phys. 131 (1990) 223-253. | MR 1065671 | Zbl 0753.35097
,[20] On a class of nonlinear Schrödinger equations, Z. Angew. Math. Phys. 43 (1992) 270-291. | MR 1162728 | Zbl 0763.35087
,[21] On concentration of positive bound states of nonlinear Schrödinger equations, Comm. Math. Phys. 153 (1993) 229-244. | MR 1218300 | Zbl 0795.35118
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