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Small perturbation of a semilinear pseudo-parabolic equation
Rotating periodic solutions of second order dissipative dynamical systems
1. | School of Mathematics and Statistics, & Center for Mathematics and Interdisciplinary Sciences, Northeast Normal University, Changchun, 130024, China |
2. | College of Mathematics, Jilin University, Changchun, 130012, China |
References:
[1] |
A. Ambrosetti and V. Coti Zelati, Periodic Solutions of Singular Lagrangian Systems, Progress in Nonlinear Differential Equations and Their Applications, 10, Birkhäuser, Boston, 1993.
doi: 10.1007/978-1-4612-0319-3. |
[2] |
K. C. Chang, Methods in Nonlinear Analysis, Springer Monographs in Mathematics, Springer-Verlag, Berlin, 2005. |
[3] |
J. F. Chu, P. J. Torres and M. R. Zhang, Periodic solutions of second order non-autonomous singular dynamical systems, J. Differential Equations, 239 (2007), 196-212.
doi: 10.1016/j.jde.2007.05.007. |
[4] |
I. Ekeland, Convexity Methods in Hamiltonian Mechanics, Results in Mathematics and Related Areas, 19, Springer, Berlin, 1990.
doi: 10.1007/978-3-642-74331-3. |
[5] |
A. Fonda and R. Toader, Periodic orbits of radially symmetric Keplerian-like systems: A topological degree approach, J. Differential Equations, 244 (2008), 3235-3264.
doi: 10.1016/j.jde.2007.11.005. |
[6] |
A. Fonda and J. A. Ureña, Periodic, subharmonic, and quasi-periodic oscillations under the action of a central force, Discrete Contin. Dyn. Syst., 29 (2011), 169-192.
doi: 10.3934/dcds.2011.29.169. |
[7] |
D. Franco and P. J. Torres, Periodic solutions of singular systems without the strong force condition, Proc. Amer. Math. Soc., 136 (2008), 1229-1236.
doi: 10.1090/S0002-9939-07-09226-X. |
[8] |
D. Franco and J. R. L. Webb, Collisionless orbits of singular and non singular dynamical systems, Discrete Contin. Dyn. Syst., 15 (2006), 747-757.
doi: 10.3934/dcds.2006.15.747. |
[9] |
W. B. Gordon, Conservative dynamical systems involving strong forces, Trans. Amer. Math. Soc., 204 (1975), 113-135.
doi: 10.1090/S0002-9947-1975-0377983-1. |
[10] |
P. Habets and L. Sanchez, Periodic solutions of dissipative dynamical systems with singular potentials, Differential Integral Equations, 3 (1990), 1139-1149. |
[11] |
Y. M. Long, Index Theory for Symplectic Paths with Applications, Progress in Mathematics, 207, Birkhäuser Verlag, Basel, 2002.
doi: 10.1007/978-3-0348-8175-3. |
[12] |
J. Mawhin, Topological Degree Methods in Nonlinear Boundary Value Problems, CBMS Regional Conference Series in Mathematics, 40, American Mathematical Society, Providence, RI, 1979. |
[13] |
J. Mawhin and M. Willem, Critical Point Theory and Hamiltonian Systems, Applied Mathematical Sciences, 74, Springer-Verlag, New York, 1989.
doi: 10.1007/978-1-4757-2061-7. |
[14] |
P. Rabinowitz, Minimax Methods in Critical Point Theory with Applications to Differential Equations, CBMS Regional Conference Series in Mathematics, 65, American Mathematical Society, Providence, RI, 1986. |
[15] |
P. J. Torres, Non-collision periodic solutions of forced dynamical systems with weak singularities, Discrete Contin. Dyn. Syst., 11 (2004), 693-698.
doi: 10.3934/dcds.2004.11.693. |
[16] |
P. J. Torres, A. J. Ureña and M. Zamora, Periodic and quasi-periodic motions of a relativistic particle under a central force field, Bull. Lond. Math. Soc., 45 (2013), 140-152.
doi: 10.1112/blms/bds076. |
[17] |
J. R. Ward, Periodic solutions of first order systems, Discrete Contin. Dyn. Syst., 33 (2013), 381-389.
doi: 10.3934/dcds.2013.33.381. |
[18] |
M. R. Zhang, Periodic solutions of damped differential systems with repulsive singular forces, Proc. Amer. Math. Soc., 127 (1999), 401-407.
doi: 10.1090/S0002-9939-99-05120-5. |
show all references
References:
[1] |
A. Ambrosetti and V. Coti Zelati, Periodic Solutions of Singular Lagrangian Systems, Progress in Nonlinear Differential Equations and Their Applications, 10, Birkhäuser, Boston, 1993.
doi: 10.1007/978-1-4612-0319-3. |
[2] |
K. C. Chang, Methods in Nonlinear Analysis, Springer Monographs in Mathematics, Springer-Verlag, Berlin, 2005. |
[3] |
J. F. Chu, P. J. Torres and M. R. Zhang, Periodic solutions of second order non-autonomous singular dynamical systems, J. Differential Equations, 239 (2007), 196-212.
doi: 10.1016/j.jde.2007.05.007. |
[4] |
I. Ekeland, Convexity Methods in Hamiltonian Mechanics, Results in Mathematics and Related Areas, 19, Springer, Berlin, 1990.
doi: 10.1007/978-3-642-74331-3. |
[5] |
A. Fonda and R. Toader, Periodic orbits of radially symmetric Keplerian-like systems: A topological degree approach, J. Differential Equations, 244 (2008), 3235-3264.
doi: 10.1016/j.jde.2007.11.005. |
[6] |
A. Fonda and J. A. Ureña, Periodic, subharmonic, and quasi-periodic oscillations under the action of a central force, Discrete Contin. Dyn. Syst., 29 (2011), 169-192.
doi: 10.3934/dcds.2011.29.169. |
[7] |
D. Franco and P. J. Torres, Periodic solutions of singular systems without the strong force condition, Proc. Amer. Math. Soc., 136 (2008), 1229-1236.
doi: 10.1090/S0002-9939-07-09226-X. |
[8] |
D. Franco and J. R. L. Webb, Collisionless orbits of singular and non singular dynamical systems, Discrete Contin. Dyn. Syst., 15 (2006), 747-757.
doi: 10.3934/dcds.2006.15.747. |
[9] |
W. B. Gordon, Conservative dynamical systems involving strong forces, Trans. Amer. Math. Soc., 204 (1975), 113-135.
doi: 10.1090/S0002-9947-1975-0377983-1. |
[10] |
P. Habets and L. Sanchez, Periodic solutions of dissipative dynamical systems with singular potentials, Differential Integral Equations, 3 (1990), 1139-1149. |
[11] |
Y. M. Long, Index Theory for Symplectic Paths with Applications, Progress in Mathematics, 207, Birkhäuser Verlag, Basel, 2002.
doi: 10.1007/978-3-0348-8175-3. |
[12] |
J. Mawhin, Topological Degree Methods in Nonlinear Boundary Value Problems, CBMS Regional Conference Series in Mathematics, 40, American Mathematical Society, Providence, RI, 1979. |
[13] |
J. Mawhin and M. Willem, Critical Point Theory and Hamiltonian Systems, Applied Mathematical Sciences, 74, Springer-Verlag, New York, 1989.
doi: 10.1007/978-1-4757-2061-7. |
[14] |
P. Rabinowitz, Minimax Methods in Critical Point Theory with Applications to Differential Equations, CBMS Regional Conference Series in Mathematics, 65, American Mathematical Society, Providence, RI, 1986. |
[15] |
P. J. Torres, Non-collision periodic solutions of forced dynamical systems with weak singularities, Discrete Contin. Dyn. Syst., 11 (2004), 693-698.
doi: 10.3934/dcds.2004.11.693. |
[16] |
P. J. Torres, A. J. Ureña and M. Zamora, Periodic and quasi-periodic motions of a relativistic particle under a central force field, Bull. Lond. Math. Soc., 45 (2013), 140-152.
doi: 10.1112/blms/bds076. |
[17] |
J. R. Ward, Periodic solutions of first order systems, Discrete Contin. Dyn. Syst., 33 (2013), 381-389.
doi: 10.3934/dcds.2013.33.381. |
[18] |
M. R. Zhang, Periodic solutions of damped differential systems with repulsive singular forces, Proc. Amer. Math. Soc., 127 (1999), 401-407.
doi: 10.1090/S0002-9939-99-05120-5. |
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