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On a class of reversible elliptic systems

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  • The existence of periodic and spatially heteroclinic solutions is studied for a class of semilinear elliptic partial differential equations.
    Mathematics Subject Classification: Primary: 35J46, 35J50; Secondary: 34C25, 34C37.

    Citation:

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  • [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.

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