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Study on the stability and bifurcations of limit cycles in higher-dimensional nonlinear autonomous systems
Existence and multiplicity of homoclinic orbits for second order Hamiltonian systems without (AR) condition
1. | School of Mathematics and Statistics, Southwest University, Chongqing 400715, China, China |
References:
[1] |
C. O. Alves, P. C. Carrião and O. H. Miyagaki, Existence of homoclinic orbits for asymptotically periodic systems involving Duffing-like equation, Appl. Math. Lett., 16 (2003), 639-642.
doi: doi:10.1016/S0893-9659(03)00059-4. |
[2] |
P. Bartolo, V. Benci and D. Fortunato, Abstract critical point theorems and applications to some nonlinear problems with "strong" resonance at infinity, Nonlinear Anal., 7 (1983), 981-1012.
doi: doi:10.1016/0362-546X(83)90115-3. |
[3] |
V. Coti-Zelati and P. H. Rabinowitz, Homoclinic orbits for second order Hamiltonian systems possessing superquadratic potentials, J. Amer. Math. Soc., 4 (1991), 693-727.
doi: doi:10.1090/S0894-0347-1991-1119200-3. |
[4] |
Y. H. Ding, Existence and multiplicity results for homoclinic solutions to a class of Hamiltonian systems, Nonlinear Anal., 25 (1995), 1095-1113.
doi: doi:10.1016/0362-546X(94)00229-B. |
[5] |
Y. H. Ding, Multiple homoclinics in a Hamiltonian system with asymptotically or super linear terms, Commun. Contemp. Math., 8 (2006), 453-480.
doi: doi:10.1142/S0219199706002192. |
[6] |
M. F. Furtado, L. A. Maia and E. A. B. Silva, Systems with coupling in $R^N$ for a class of noncoercive potentials, Discrete Contin. Dyn. Syst., 2003, suppl., 295-304. |
[7] |
P. L. Felmer and E. A. B. Silva, Homoclinic and periodic orbits for Hamiltonian systems, Ann. Scuola Norm. Sup. Pisa Cl. Sci., 26 (1998), 285-301. |
[8] |
P. Korman and A. C. Lazer, Homoclinic orbits for a class of symmetric Hamiltonian systems, Electron. J. Differential Equations, (1994), approx. 10 pp. |
[9] |
T. Kato, "Perturbation Theory for Linear Operators," Springer-Verlag, Berlin, 1995. |
[10] |
P. L. Lions, The concentration-compactness principle in the calculus of variations. The locally compact case II, Ann. Inst. H. Poincaré Anal. Non Linéaire, 1 (1984), 223-283. |
[11] |
Y. Lv and C. L. Tang, Existence of even homoclinic orbits for second-order Hamiltonian systems, Nonlinear Anal., 67 (2007), 2189-2198.
doi: doi:10.1016/j.na.2006.08.043. |
[12] |
W. Omana and M. Willem, Homoclinic orbits for a class of Hamiltonian systems, Differential Integral Equations, 5 (1992), 1115-1120. |
[13] |
Z. Q. Ou and C. L. Tang, Existence of homoclinic solution for the second order Hamiltonian systems, J. Math. Anal. Appl., 291 (2004), 203-213.
doi: doi:10.1016/j.jmaa.2003.10.026. |
[14] |
P. H. Rabinowitz, Homoclinic orbits for a class of Hamiltonian systems, Proc. Roy. Soc. Edinburgh Sect. A, 114 (1990), 33-38. |
[15] |
P. H. Rabinowitz and K. Tanaka, Some results on connecting orbits for a class of Hamiltonian systems, Math. Z., 206 (1991), 473-499.
doi: doi:10.1007/BF02571356. |
[16] |
P. H. Rabinowitz, Homoclinic and heteroclinic orbits for a class of Hamiltonian systems, Calc. Variations, 1 (1993), 1-36.
doi: doi:10.1007/BF02163262. |
[17] |
M. Willem, "Minimax Theorems," 24, Birkhäuser Boston, Inc., Boston, MA, 1996. |
[18] |
J. Yang and F. B. Zhao, Infinitely many homoclinic orbits for the second-order Hamiltonian systems with super-quadratic potentials, Nonlinear Analysis: Real World Applications, 10 (2009), 1417-1423.
doi: doi:10.1016/j.nonrwa.2008.01.013. |
[19] |
W. M. Zou and S. J. Li, Infinitely many homoclinic orbits for the second-order hamiltonian systems, Appl. Math. Lett., 16 (2003), 1283-1287.
doi: doi:10.1016/S0893-9659(03)90130-3. |
[20] |
W. M. Zou, Variant fountain theorems and their applications, Manuscripta Math., 104 (2001), 343-358.
doi: doi:10.1007/s002290170032. |
show all references
References:
[1] |
C. O. Alves, P. C. Carrião and O. H. Miyagaki, Existence of homoclinic orbits for asymptotically periodic systems involving Duffing-like equation, Appl. Math. Lett., 16 (2003), 639-642.
doi: doi:10.1016/S0893-9659(03)00059-4. |
[2] |
P. Bartolo, V. Benci and D. Fortunato, Abstract critical point theorems and applications to some nonlinear problems with "strong" resonance at infinity, Nonlinear Anal., 7 (1983), 981-1012.
doi: doi:10.1016/0362-546X(83)90115-3. |
[3] |
V. Coti-Zelati and P. H. Rabinowitz, Homoclinic orbits for second order Hamiltonian systems possessing superquadratic potentials, J. Amer. Math. Soc., 4 (1991), 693-727.
doi: doi:10.1090/S0894-0347-1991-1119200-3. |
[4] |
Y. H. Ding, Existence and multiplicity results for homoclinic solutions to a class of Hamiltonian systems, Nonlinear Anal., 25 (1995), 1095-1113.
doi: doi:10.1016/0362-546X(94)00229-B. |
[5] |
Y. H. Ding, Multiple homoclinics in a Hamiltonian system with asymptotically or super linear terms, Commun. Contemp. Math., 8 (2006), 453-480.
doi: doi:10.1142/S0219199706002192. |
[6] |
M. F. Furtado, L. A. Maia and E. A. B. Silva, Systems with coupling in $R^N$ for a class of noncoercive potentials, Discrete Contin. Dyn. Syst., 2003, suppl., 295-304. |
[7] |
P. L. Felmer and E. A. B. Silva, Homoclinic and periodic orbits for Hamiltonian systems, Ann. Scuola Norm. Sup. Pisa Cl. Sci., 26 (1998), 285-301. |
[8] |
P. Korman and A. C. Lazer, Homoclinic orbits for a class of symmetric Hamiltonian systems, Electron. J. Differential Equations, (1994), approx. 10 pp. |
[9] |
T. Kato, "Perturbation Theory for Linear Operators," Springer-Verlag, Berlin, 1995. |
[10] |
P. L. Lions, The concentration-compactness principle in the calculus of variations. The locally compact case II, Ann. Inst. H. Poincaré Anal. Non Linéaire, 1 (1984), 223-283. |
[11] |
Y. Lv and C. L. Tang, Existence of even homoclinic orbits for second-order Hamiltonian systems, Nonlinear Anal., 67 (2007), 2189-2198.
doi: doi:10.1016/j.na.2006.08.043. |
[12] |
W. Omana and M. Willem, Homoclinic orbits for a class of Hamiltonian systems, Differential Integral Equations, 5 (1992), 1115-1120. |
[13] |
Z. Q. Ou and C. L. Tang, Existence of homoclinic solution for the second order Hamiltonian systems, J. Math. Anal. Appl., 291 (2004), 203-213.
doi: doi:10.1016/j.jmaa.2003.10.026. |
[14] |
P. H. Rabinowitz, Homoclinic orbits for a class of Hamiltonian systems, Proc. Roy. Soc. Edinburgh Sect. A, 114 (1990), 33-38. |
[15] |
P. H. Rabinowitz and K. Tanaka, Some results on connecting orbits for a class of Hamiltonian systems, Math. Z., 206 (1991), 473-499.
doi: doi:10.1007/BF02571356. |
[16] |
P. H. Rabinowitz, Homoclinic and heteroclinic orbits for a class of Hamiltonian systems, Calc. Variations, 1 (1993), 1-36.
doi: doi:10.1007/BF02163262. |
[17] |
M. Willem, "Minimax Theorems," 24, Birkhäuser Boston, Inc., Boston, MA, 1996. |
[18] |
J. Yang and F. B. Zhao, Infinitely many homoclinic orbits for the second-order Hamiltonian systems with super-quadratic potentials, Nonlinear Analysis: Real World Applications, 10 (2009), 1417-1423.
doi: doi:10.1016/j.nonrwa.2008.01.013. |
[19] |
W. M. Zou and S. J. Li, Infinitely many homoclinic orbits for the second-order hamiltonian systems, Appl. Math. Lett., 16 (2003), 1283-1287.
doi: doi:10.1016/S0893-9659(03)90130-3. |
[20] |
W. M. Zou, Variant fountain theorems and their applications, Manuscripta Math., 104 (2001), 343-358.
doi: doi:10.1007/s002290170032. |
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