Citation: Paul H. Rabinowitz. On a class of reversible elliptic systems[J]. Networks and Heterogeneous Media, 2012, 7(4): 927-939. doi: 10.3934/nhm.2012.7.927
[1] |
S. Aubry and P. Y. LeDaeron, The discrete Frenkel-Kantorova model and its extensions I-Exact results for the ground states, Physica, 8D, (1983), 381-422. doi: 10.1016/0167-2789(83)90233-6
![]() |
[2] |
J. Mather, Existence of quasi-periodic orbits for twist homeomorphisms of the annulus, Topology, 21, (1982), 457-467. doi: 10.1016/0040-9383(82)90023-4
![]() |
[3] | J. Mather, Variational construction of connecting orbits, Ann. Inst. Fourier ;(Grenoble), 43, (1993), 1349-1386. |
[4] | J. Moser, Minimal solutions of variational problems on a torus, Ann. Inst. Poincare, Anal. Non Lineaire, 3 (1986), 229-272. |
[5] | V. Bangert, On minimal laminations of the torus, Ann. Inst. H. Poincaré, Anal. Non Lineaire, 6 (1989), 95-138. |
[6] |
P. Rabinowitz and E. Stredulinsky, "Extensions of Moser-Bangert Theory: Locally Minimal Solutions," Progress in Nonlinear Differential Equations and Their Applications, 81, Birkhauser, Boston, 2011. doi: 10.1007/978-0-8176-8117-3
![]() |
[7] |
U. Bessi, Many solutions of elliptic problems on $\mathbbR^n$ of irrational slope, Comm. Partial Differential Equations, 30 (2005), 1773-1804. doi: 10.1080/03605300500299992
![]() |
[8] |
U. Bessi, Slope-changing solutions of elliptic problems on $\mathbbR^n$, Nonlinear Anal., 68 (2008), 3923-3947. doi: 10.1016/j.na.2007.04.031
![]() |
[9] |
F. Alessio, L. Jeanjean and P. Montecchiari, Stationary layered solutions in $\mathbbR^{2}$ for a class of non autonomous Allen-Cahn equations, Calc. Var. Partial Differential Equations, 11 (2000), 177-202. doi: 10.1007/s005260000036
![]() |
[10] |
F. Alessio, L. Jeanjean and P. Montecchiari, Existence of infinitely many stationary layered solutions in $\mathbbR^{2}$ for a class of periodic Allen-Cahn equations, Comm. Partial Differential Equations, 27 (2002), 1537-1574. doi: 10.1081/PDE-120005848
![]() |
[11] |
F. Alessio and P. Montecchiari, Entire solutions in $\mathbbR^{2}$ for a class of Allen-Cahn equations, ESAIM Control Optim. Calc. Var., 11 (2005), 633-672. doi: 10.1051/cocv:2005023
![]() |
[12] | F. Alessio and P. Montecchiari, Multiplicity of entire solutions for a class of almost periodic Allen-Cahn type equations, Adv. Nonlinear Stud., 5 (2005), 515-549. |
[13] |
M. Novaga and E. Valdinoci, Bump solutions for the mesoscopic Allen-Cahn equation in periodic media, Calc. Var. Partial Differential Equations, 40 (2011), 37-49. doi: 10.1007/s00526-010-0332-4
![]() |
[14] |
R. de la Llave and E. Valdinoci, Multiplicity results for interfaces of Ginzburg-Landau Allen-Cahn equations in periodic media, Adv. Math., 215 (2007), 379-426. doi: 10.1016/j.aim.2007.03.013
![]() |
[15] |
R. de la Llave and E. Valdinoci, A generalization of Aubry-Mather theory to partial differential equations and pseudo-differential equations, Ann. Inst. H. Poincaré Anal. Non Lineaire, 26 (2009), 1309-1344. doi: 10.1016/j.anihpc.2008.11.002
![]() |
[16] |
E. Valdinoci, Plane-like minimizers in periodic media: Jet flows and Ginzburg-Landau-type functionals, J. Reine Angew. Math., 574 (2004), 147-185. doi: 10.1515/crll.2004.068
![]() |
[17] | D. Gilbarg and N. Trudinger, "Elliptic Partial Differential Equations of Second Order," Second edition, Grundlehren, 224, Springer, Berlin, Heidelberg, New York and Tokyo, 1983. |
[18] |
P. Rabinowitz and E. Stredulinsky, On some results of Moser and of Bangert, Ann. Inst. H. Poincare Anal. Non Lineaire, 21 (2004), 673-688. doi: 10.1016/j.anihpc.2003.10.002
![]() |
[19] | P. Rabinowitz and E. Stredulinsky, On some results of Moser and of Bangert. II, Adv. Nonlinear Stud., 4 (2004), 377-396. |
[20] | S. Bolotin, Existence of homoclinic motions. (Russian), Vestnik Moskov. Univ., Ser. I Mat. Mekh., (1983), 98-103. |
[21] | A. Anane, O. Chakrone, Z. El Allali and I. Hadi., A unique continuation property for linear elliptic systems and nonresonance problems, Electron. J. Differential Equations, (2001), 20 pp. (electronic). |
[22] | M. Protter, Unique continuation for elliptic equations, Trans. Amer. Math. Soc., 95 (1960), 81-91. |
[23] | R. Pederson, On the unique continuation theorem for certain second and fourth order equations, Comm. Pure Appl. Math., 11 (1958), 67-80. |
[24] |
P. Rabinowitz, Heteroclinics for a reversible Hamiltonian system, Ergodic Theory Dynam. Systems, 14 (1994), 817-829. doi: 10.1017/S0143385700008178
![]() |
[25] | P. Rabinowitz, A note on a class of reversible Hamiltonian systems, Adv. Nonlinear Stud., 9 (2009), 815-823. |
[26] |
T. Maxwell, Heteroclinic chains for a reversible Hamiltonian system, Nonlinear Analysis, T.M.A., 28 (1997), 871-887. doi: 10.1016/0362-546X(95)00193-Y
![]() |
[27] | R. Adams, "Sobolev Spaces," Pure and Applied Mathematics, 65, Academic Press, New York and London, 1975. |