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Existence of solutions for nonlinear operator equations
1. | School of Mathematical Science, Nanjing Normal University, Nanjing 210023, China |
2. | Danyang Normal School, Zhenjiang College, Zhenjiang 212300, China |
We investigate solutions for nonlinear operator equations and obtain some abstract existence results by linking methods. Some well-known theorems about periodic solutions for second-order Hamiltonian systems by M. Schechter are special cases of these results.
References:
[1] |
G. Bonanno, R. Livrea and M. Schechter,
Multiple solutions of second order Hamiltonian systems, Electron. J. Qual. Theory Differ. Equ., 33 (2017), 1-15.
doi: 10.14232/ejqtde.2017.1.33. |
[2] |
Y. Chen, Y. Dong and Y. Shan,
Existence of solutions for sublinear or superlinear operator equations, Sci. China Math., 58 (2015), 1653-1664.
doi: 10.1007/s11425-014-4966-0. |
[3] | Y. Dong, Index Theory for Hamiltonian Systems and Multiple Solutions Problems, Science Press, Beijing, 2014. Google Scholar |
[4] |
L. Li and M. Schechter,
Existence of solutions for second order Hamiltonian systems, Nonlinear Anal. Real World Appl., 27 (2016), 283-296.
doi: 10.1016/j.nonrwa.2015.08.001. |
[5] |
J. Pipan and M. Schechter,
Non-autonomous second order Hamiltonian systems, J. Differential Equations, 257 (2014), 351-373.
doi: 10.1016/j.jde.2014.03.016. |
[6] |
M. Schechter, Periodic solutions of second-order nonautonomous dynamical systems, Bound. Value Probl., 2006 (2006), Art. ID 25104, 9pp.
doi: 10.1155/bvp/2006/25104. |
[7] |
M. Schechter,
Periodic non-autonomous second order dynamical systems, J. Differential Equations, 223 (2006), 290-302.
doi: 10.1016/j.jde.2005.02.022. |
[8] |
M. Schechter, Minmax Systems and Critical Point Theory, Birkh$\ddot{a}$user, Boston, 2009. Google Scholar |
[9] |
M. Schechter, Linking Methods in Critical Point Theory, Birkh$\ddot{a}$user, Boston, 1999. Google Scholar |
[10] |
M. Schechter,
Nonautonomous second order Hamiltonian systems, Pacific J. Math., 251 (2011), 431-452.
doi: 10.2140/pjm.2011.251.431. |
[11] |
Z. Wang and J. Zhang,
New existence results on periodic solutions of non-autonomous second order Hamiltonian systems, Appl. Math. Lett., 79 (2018), 43-50.
doi: 10.1016/j.aml.2017.11.016. |
[12] |
X. Zhang and X. Tang,
Some united existence results of periodic solutions for non-quadratic second order Hamiltonian systems, Commun. Pure Appl. Anal., 13 (2014), 75-95.
doi: 10.3934/cpaa.2014.13.75. |
[13] |
W. Zou and S. Li,
On Schechter's linking theorems, J. Funct. Anal., 258 (2010), 3347-3361.
doi: 10.1016/j.jfa.2009.11.005. |
show all references
References:
[1] |
G. Bonanno, R. Livrea and M. Schechter,
Multiple solutions of second order Hamiltonian systems, Electron. J. Qual. Theory Differ. Equ., 33 (2017), 1-15.
doi: 10.14232/ejqtde.2017.1.33. |
[2] |
Y. Chen, Y. Dong and Y. Shan,
Existence of solutions for sublinear or superlinear operator equations, Sci. China Math., 58 (2015), 1653-1664.
doi: 10.1007/s11425-014-4966-0. |
[3] | Y. Dong, Index Theory for Hamiltonian Systems and Multiple Solutions Problems, Science Press, Beijing, 2014. Google Scholar |
[4] |
L. Li and M. Schechter,
Existence of solutions for second order Hamiltonian systems, Nonlinear Anal. Real World Appl., 27 (2016), 283-296.
doi: 10.1016/j.nonrwa.2015.08.001. |
[5] |
J. Pipan and M. Schechter,
Non-autonomous second order Hamiltonian systems, J. Differential Equations, 257 (2014), 351-373.
doi: 10.1016/j.jde.2014.03.016. |
[6] |
M. Schechter, Periodic solutions of second-order nonautonomous dynamical systems, Bound. Value Probl., 2006 (2006), Art. ID 25104, 9pp.
doi: 10.1155/bvp/2006/25104. |
[7] |
M. Schechter,
Periodic non-autonomous second order dynamical systems, J. Differential Equations, 223 (2006), 290-302.
doi: 10.1016/j.jde.2005.02.022. |
[8] |
M. Schechter, Minmax Systems and Critical Point Theory, Birkh$\ddot{a}$user, Boston, 2009. Google Scholar |
[9] |
M. Schechter, Linking Methods in Critical Point Theory, Birkh$\ddot{a}$user, Boston, 1999. Google Scholar |
[10] |
M. Schechter,
Nonautonomous second order Hamiltonian systems, Pacific J. Math., 251 (2011), 431-452.
doi: 10.2140/pjm.2011.251.431. |
[11] |
Z. Wang and J. Zhang,
New existence results on periodic solutions of non-autonomous second order Hamiltonian systems, Appl. Math. Lett., 79 (2018), 43-50.
doi: 10.1016/j.aml.2017.11.016. |
[12] |
X. Zhang and X. Tang,
Some united existence results of periodic solutions for non-quadratic second order Hamiltonian systems, Commun. Pure Appl. Anal., 13 (2014), 75-95.
doi: 10.3934/cpaa.2014.13.75. |
[13] |
W. Zou and S. Li,
On Schechter's linking theorems, J. Funct. Anal., 258 (2010), 3347-3361.
doi: 10.1016/j.jfa.2009.11.005. |
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