High-energy solutions for a phase transition problem

Journal of Differential Equations

Volumn 194, Issue 1, 2003, Pages 198-220

  Felmer, Patricio L ^a   Martinez, Salomé ^b  

^a UNIVERSITY OF CHILE   (Chile)

^b GEORGIA INSTITUTE OF TECHNOLOGY   (United States)

Author keywords

Highly oscillatory solutions; Phase transition; Variational methods

Indexed keywords

EID: 0141726763     PISSN: 00220396     EISSN: None     Source Type: Journal    
DOI: 10.1016/S0022-0396(03)00194-3     Document Type: Article

References (13)

1. S. Ai, Multi-pulse like orbits for a singularly perturbed nearly integrable system, J. Differential Equations 179 (2002) 384-432.
2. S. Ai, On a boundary value problem of a singularly perturbed O.D.E, J. Math. Anal. Appl. 277 (2003) 405-422.
3. S. Ai, S. Hastings, A shooting approach to layers and chaos in a forced Duffing equation, J. Differential Equations 185 (2002) 389-436.
4. N. Alikakos, P. Bates, G. Fusco, Solutions to the nonautonomous bistable equation with specified Morse index. I. Existence, Trans. Amer. Math. Soc. 340 (2) (1993) 641-654.
5. S. Angenent, J. Mallet-Paret, L. Peletier, Stable transition layer in a semilinear boundary value problem, J. Differential Equations 67 (1987) 212-242.
6. M. del Pino, P. Felmer, K. Tanaka, An elementary construction of complex patterns in nonlinear Schrödinger equations, Nonlinearity 15 (2002) 1653-1671.
7. P. Felmer, J.J. Torres, Semi classical limits for the one dimensional nonlinear Schrödinger equation, Comm. Contemp. Math. 4 (2002) 481-512.
8. T. Gedeon, H. Kokubu, K. Mischaikow, H. Oka, Chaotic solutions in slowly varying perturbations of Hamiltonian systems with applications to shallow water sloshing, J. Dynam. Differential Equations 14 (2002) 63-84.
9. J. Hale, K. Sakamoto, Existence and stability of transition layers, Japan J. Appl. Math. 5 (3) (1988) 287-303.
10. K. Nakashima, Multi-layered stationary solutions for a spatially inhomogeneous Allen-Cahn equation, J. Differential Equations 191 (2003) 234-276.
11. K. Nakashima, Stable transition layers in a balanced bistable equation, Differential Integral Equations 13 (7-9) (2000) 1025-1038.
12. K. Nakashima, K. Tanaka, Clustering layers and boundary layers in spatially inhomogeneous phase transition problems, Ann. Inst. H. Poincaré Anal. Non Linéaire 20 (2003) 107-143.
13. P. Rabinowitz, Minimax Methods in Critical Point Theory with Applications to Differential Equations, American Mathematical Society Conference Series in Mathematics, Vol. 65, American Mathematical Society, Providence, RI, 1986.