Nonlinear Oscillations of Hamiltonian PDEs
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[1] Pavel I. Plotnikov,et al. Standing Waves on an Infinitely Deep Perfect Fluid Under Gravity , 2005 .
[2] Sergiu Klainerman,et al. Long-time behavior of solutions to nonlinear evolution equations , 1982 .
[3] I. Ekeland,et al. Convex Hamiltonian energy surfaces and their periodic trajectories , 1987 .
[4] Luigi Chierchia,et al. KAM Tori for 1D Nonlinear Wave Equations¶with Periodic Boundary Conditions , 1999, chao-dyn/9904036.
[5] Sergiu Klainerman,et al. Global existence for nonlinear wave equations , 1980 .
[6] Jean-Michel Coron,et al. Periodic solutions of a nonlinear wave equation without assumption of monotonicity , 1983 .
[7] C. Conley,et al. An index theory for periodic solutions of a Hamiltonian system , 1983 .
[8] I. Ekeland,et al. Symmetry breaking in Hamiltonian systems , 1987 .
[9] L. Nirenberg,et al. On elliptic partial differential equations , 1959 .
[10] D. C. Lewis,et al. On the periodic motions near a given periodic motion of a dynamical system , 1934 .
[11] Jean-Michel Coron,et al. Free vibrations for a nonlinear wave equation and a theorem of P. Rabinowitz , 1980 .
[12] Vieri Benci,et al. Critical point theorems for indefinite functionals , 1979 .
[13] Yiming Long,et al. Closed characteristics on compact convex hypersurfaces in $\R^{2n}$ , 2001 .
[14] V. Arnold. Mathematical Methods of Classical Mechanics , 1974 .
[15] Hana Lovicarová. Periodic solutions of a weakly nonlinear wave equation in one dimension , 1969 .
[16] E. Zehnder,et al. Generalized implicit function theorems with applications to some small divisor problems, I , 1976 .
[17] Charles Pugh,et al. The C1 Closing Lemma, including Hamiltonians , 1983, Ergodic Theory and Dynamical Systems.
[18] P. J. McKenna. On solutions of a nonlinear wave question when the ratio of the period to the length of the interval is irrational , 1985 .
[19] I. Ekeland,et al. On the number of periodic trajectories for a Hamiltonian flow on a convex energy surface , 1980 .
[20] Jean Bourgain,et al. QUASI-PERIODIC SOLUTIONS OF HAMILTONIAN PERTURBATIONS OF 2D LINEAR SCHRODINGER EQUATIONS , 1998 .
[21] Tosio Kato. Perturbation theory for linear operators , 1966 .
[22] Jürgen Moser,et al. A rapidly convergent iteration method and non-linear differential equations = II , 1966 .
[23] P. Rabinowitz,et al. Dual variational methods in critical point theory and applications , 1973 .
[24] Jürgen Moser,et al. Convergent series expansions for quasi-periodic motions , 1967 .
[25] Michael Struwe,et al. Variational methods: Applications to nonlinear partial differential equations and Hamiltonian systems , 1990 .
[26] V. Arnold. SMALL DENOMINATORS AND PROBLEMS OF STABILITY OF MOTION IN CLASSICAL AND CELESTIAL MECHANICS , 1963 .
[27] P. Rabinowitz. Minimax methods in critical point theory with applications to differential equations , 1986 .
[28] Yanheng Ding,et al. Periodic solutions of a Dirac equation with concave and convex nonlinearities , 1999 .
[29] J. Schwartz. Nonlinear Functional Analysis , 1969 .
[30] Sergei Kuksin,et al. Hamiltonian perturbations of infinite-dimensional linear systems with an imaginary spectrum , 1987 .
[31] Xiaoping Yuan,et al. Quasi-periodic solutions of completely resonant nonlinear wave equations ✩ , 2006 .
[32] B. Lidskii,et al. Periodic solutions of the equation utt — uxx + u3 = 0 , 1988 .
[33] I. Ekeland. Convexity Methods In Hamiltonian Mechanics , 1990 .
[34] H. Amann,et al. Nontrivial solutions for a class of nonresonance problems and applications to nonlinear differential equations , 1980 .
[35] P. Rabinowitz,et al. Generalized cohomological index theories for Lie group actions with an application to bifurcation questions for Hamiltonian systems , 1977 .
[36] Antonio Ambrosetti,et al. Nonlinear Analysis and Semilinear Elliptic Problems , 2007 .
[37] Walter Craig,et al. Numerical simulation of gravity waves , 1993 .
[38] F. Sergeraert. Un théorème de fonctions implicites sur certains espaces de Fréchet et quelques applications , 1972 .
[39] Vladimir E. Zakharov,et al. Stability of periodic waves of finite amplitude on the surface of a deep fluid , 1968 .
[40] Alan Weinstein,et al. Periodic Orbits for Convex Hamiltonian Systems , 1978 .
[41] Luca Biasco,et al. Time Periodic Solutions for the Nonlinear Wave Equation with Long Minimal Period , 2006, SIAM J. Math. Anal..
[42] Louis Nirenberg,et al. Topics in Nonlinear Functional Analysis , 2001 .
[43] M. Willem. Density of the Range of Potential-operators , 1981 .
[44] J. Mawhin,et al. Critical Point Theory and Hamiltonian Systems , 1989 .
[45] D. Saari,et al. Stable and Random Motions in Dynamical Systems , 1975 .
[46] Periodic solutions of wave equations for asymptotically full measure sets of frequencies , 2005, math/0512053.
[47] P. Rabinowitz. Time periodic solutions of nonlinear wave equations , 1971 .
[48] T. Bartsch. A generalization of the Weinstein-Moser theorems on periodic orbits of a hamiltonian system near an equilibrium , 1997 .
[49] E. T.. An Introduction to the Theory of Numbers , 1946, Nature.
[50] Haim Brezis,et al. Remarks on finding critical points , 1991 .
[51] J. Moser,et al. A NEW TECHNIQUE FOR THE CONSTRUCTION OF SOLUTIONS OF NONLINEAR DIFFERENTIAL EQUATIONS. , 1961, Proceedings of the National Academy of Sciences of the United States of America.
[52] Alan Weinstein,et al. Normal modes for nonlinear hamiltonian systems , 1973 .
[53] Dario Bambusi,et al. Families of Periodic Solutions of Resonant PDEs , 2001, J. Nonlinear Sci..
[54] E. Wright,et al. An Introduction to the Theory of Numbers , 1939 .
[55] J. Moser. A rapidly convergent iteration method and non-linear partial differential equations - I , 1966 .
[56] Jürgen Moser,et al. Periodic orbits near an equilibrium and a theorem by Alan Weinstein , 1976 .
[57] Haim Brezis,et al. Periodic solutions of nonlinear vibrating strings and duality principles , 1983 .
[58] P. Holmes,et al. Nonlinear Oscillations, Dynamical Systems, and Bifurcations of Vector Fields , 1983, Applied Mathematical Sciences.
[59] Guido Gentile,et al. Conservation of Resonant Periodic Solutions for the One-Dimensional Nonlinear Schrödinger Equation , 2006 .
[60] L. Hörmander,et al. The boundary problems of physical geodesy , 1976 .
[61] K. Deimling. Nonlinear functional analysis , 1985 .
[62] S. B. Kuksin. Analysis of Hamiltonian PDEs , 2000 .
[63] Walter Craig,et al. Newton's method and periodic solutions of nonlinear wave equations , 1993 .
[64] E. Valdinoci,et al. Periodic Orbits Close to Elliptic Tori and Applications to the Three-body Problem , 2003, math/0304103.
[65] P. Rabinowitz. A bifurcation theorem for potential operators , 1977 .
[66] A. Ambrosetti,et al. Homoclinics: Poincaré-Melnikov type results via a variational approach , 1998 .
[67] M. Gromov. SMOOTHING AND INVERSION OF DIFFERENTIAL OPERATORS , 1972 .
[68] L. Biasco,et al. Periodic solutions of nonlinear wave equations with non-monotone forcing terms , 2005 .
[69] J. Pöschel,et al. Quasi-periodic solutions for a nonlinear wave equation , 1996 .
[70] J. Pöschel,et al. Inverse spectral theory , 1986 .
[71] M. Berti,et al. Multiplicity of periodic solutions of nonlinear wave equations , 2004 .
[72] P. Rabinowitz,et al. Periodic Solutions of Nonlinear Hyperbolie Partial Differential Equations , 1967 .
[73] Eduard Zehnder,et al. Symplectic Invariants and Hamiltonian Dynamics , 1994 .
[74] S. Smale,et al. A generalized Morse theory , 1964 .
[75] Richard S. Hamilton,et al. The inverse function theorem of Nash and Moser , 1982 .
[76] M. Berti,et al. Cantor families of periodic solutions for wave equations via a variational principle , 2008 .
[77] J. T. Beale,et al. The existence of solitary water waves , 1977 .
[78] J. Mawhin,et al. Diophantine approximation, Bessel functions and radially symmetric periodic solutions of semilinear wave equations in a ball , 2001 .
[79] J. Bourgain. Construction of periodic solutions of nonlinear wave equations in higher dimension , 1995 .
[80] P. Lax. Outline of a theory of the KdV equation , 1996 .
[81] Jürgen Moser,et al. Lectures on Celestial Mechanics , 1971 .
[82] J. Moser. Addendum to “periodic orbits near an equilibrium and a theorem by alan weinstein” , 1978 .
[83] Louis Jeanjean,et al. On the existence of bounded Palais–Smale sequences and application to a Landesman–Lazer-type problem set on ℝN , 1999, Proceedings of the Royal Society of Edinburgh: Section A Mathematics.
[84] M. Procesi. QUASI-PERIODIC SOLUTIONS FOR COMPLETELY RESONANT NON-LINEAR WAVE EQUATIONS IN 1D AND 2D , 2005 .
[85] Massimiliano Berti,et al. Periodic Solutions of Nonlinear Wave Equations with General Nonlinearities , 2002, math/0211310.
[86] A stability theorem for the obstacle problem , 1975 .
[87] A. Ambrosetti,et al. A primer of nonlinear analysis , 1993 .
[88] Cantor families of periodic solutions for completely resonant nonlinear wave equations , 2004, math/0410618.
[89] C. Eugene Wayne,et al. Periodic and quasi-periodic solutions of nonlinear wave equations via KAM theory , 1990 .
[90] Paul H. Rabinowitz,et al. Periodic solutions of hamiltonian systems , 1978 .
[91] J. Pöschel,et al. Invariant Cantor manifolds of quasi-periodic oscillations for a nonlinear Schrodinger equation , 1996 .
[92] Jean-Marcel Fokam. Forced Vibrations via Nash-Moser Iteration , 2008 .
[93] A. Ambrosetti. Critical points and nonlinear variational problems , 1992 .
[94] Michela Procesi,et al. Quasi-Periodic Solutions of Completely Resonant Forced Wave Equations , 2005, math/0504406.
[95] Jean Bourgain,et al. Construction of quasi-periodic solutions for Hamiltonian perturbations of linear equations and applications to nonlinear PDE , 1994 .