메뉴 건너뛰기
Journal of Differential Equations
Volumn 251, Issue 4-5, 2011, Pages 816-833
Infinitely many periodic solutions for second order Hamiltonian systems
Author keywords

Asymptotically quadratic; Periodic solution; Second order Hamiltonian system; Superquadratic
Indexed keywords

EID: 79958200206     PISSN: 00220396     EISSN: 10902732     Source Type: Journal    
DOI: 10.1016/j.jde.2011.05.021     Document Type: Article
Times cited : (40)
References (28)
  • 1
    • 0000100228 scopus 로고
    • Periodic solutions of asymptotically linear Hamiltonian systems
    • Amann H., Zehnder E. Periodic solutions of asymptotically linear Hamiltonian systems. Manuscripta Math. 1980, 32:149-189.
    • (1980) Manuscripta Math. , vol.32 , pp. 149-189
    • Amann, H.1    Zehnder, E.2
  • 2
    • 0031374745 scopus 로고    scopus 로고
    • Existence of periodic solutions of Hamiltonian systems with potential indefinite in sign
    • Antonacci F. Existence of periodic solutions of Hamiltonian systems with potential indefinite in sign. Nonlinear Anal. 1997, 29:1353-1364.
    • (1997) Nonlinear Anal. , vol.29 , pp. 1353-1364
    • Antonacci, F.1
  • 3
    • 0012323136 scopus 로고    scopus 로고
    • Second order nonautonomous systems with symmetric potential changing sign
    • Antonacci F., Magrone P. Second order nonautonomous systems with symmetric potential changing sign. Rend. Mat. Appl. 1998, 18:367-379.
    • (1998) Rend. Mat. Appl. , vol.18 , pp. 367-379
    • Antonacci, F.1    Magrone, P.2
  • 4
    • 0001341245 scopus 로고
    • Forced vibrations of superquadratic Hamiltonian systems
    • Bahri A., Berestycki H. Forced vibrations of superquadratic Hamiltonian systems. Acta Math. 1984, 152:143-197.
    • (1984) Acta Math. , vol.152 , pp. 143-197
    • Bahri, A.1    Berestycki, H.2
  • 5
    • 0001232950 scopus 로고
    • On critical point theory for indefinite functionals in the presence of symmetries
    • Benci V. On critical point theory for indefinite functionals in the presence of symmetries. Trans. Amer. Math. Soc. 1982, 274:533-572.
    • (1982) Trans. Amer. Math. Soc. , vol.274 , pp. 533-572
    • Benci, V.1
  • 6
    • 1542437218 scopus 로고
    • Critical point theorems for indefinite functionals
    • Benci V., Rabinowitz P.H. Critical point theorems for indefinite functionals. Invent. Math. 1979, 52:241-273.
    • (1979) Invent. Math. , vol.52 , pp. 241-273
    • Benci, V.1    Rabinowitz, P.H.2
  • 7
    • 0034353702 scopus 로고    scopus 로고
    • Periodic solutions of Hamiltonian systems
    • Ding Y., Lee C. Periodic solutions of Hamiltonian systems. SIAM J. Math. Anal. 2000, 32:555-571.
    • (2000) SIAM J. Math. Anal. , vol.32 , pp. 555-571
    • Ding, Y.1    Lee, C.2
  • 8
    • 0000060673 scopus 로고
    • Periodic and homoclinic solutions to a class of Hamiltonian systems with the potentials changing sign
    • Ding Y., Girardi M. Periodic and homoclinic solutions to a class of Hamiltonian systems with the potentials changing sign. Dynam. Systems Appl. 1993, 2:131-145.
    • (1993) Dynam. Systems Appl. , vol.2 , pp. 131-145
    • Ding, Y.1    Girardi, M.2
  • 9
    • 38249006566 scopus 로고
    • Periodic solutions of "superquadratic" Hamiltonian systems
    • Felmer P.L. Periodic solutions of "superquadratic" Hamiltonian systems. J. Differential Equations 1993, 102:188-207.
    • (1993) J. Differential Equations , vol.102 , pp. 188-207
    • Felmer, P.L.1
  • 10
    • 0007062478 scopus 로고    scopus 로고
    • Multiplicity for symmetric indefinite functionals: application to Hamiltonian and elliptic systems
    • Felmer P.L., Wang Z.Q. Multiplicity for symmetric indefinite functionals: application to Hamiltonian and elliptic systems. Topol. Methods Nonlinear Anal. 1998, 12:207-226.
    • (1998) Topol. Methods Nonlinear Anal. , vol.12 , pp. 207-226
    • Felmer, P.L.1    Wang, Z.Q.2
  • 11
    • 0001832075 scopus 로고
    • Existence and multiplicity results for periodic solutions of superquadratic Hamiltonian systems where the potential changes sign
    • Girardi M., Matzeu M. Existence and multiplicity results for periodic solutions of superquadratic Hamiltonian systems where the potential changes sign. NoDEA Nonlinear Differential Equations Appl. 1995, 2:35-61.
    • (1995) NoDEA Nonlinear Differential Equations Appl. , vol.2 , pp. 35-61
    • Girardi, M.1    Matzeu, M.2
  • 12
    • 0003095840 scopus 로고
    • Periodic solutions of a second order superquadratic system with a change of sign in the potential
    • Lassoued L. Periodic solutions of a second order superquadratic system with a change of sign in the potential. J. Differential Equations 1991, 93:1-18.
    • (1991) J. Differential Equations , vol.93 , pp. 1-18
    • Lassoued, L.1
  • 13
    • 0003106929 scopus 로고
    • Morse theory and asymptotic linear Hamiltonian system
    • Li S., Liu J. Morse theory and asymptotic linear Hamiltonian system. J. Differential Equations 1989, 78:53-73.
    • (1989) J. Differential Equations , vol.78 , pp. 53-73
    • Li, S.1    Liu, J.2
  • 14
    • 0001000911 scopus 로고
    • Multiple solutions of perturbed superquadratic second order Hamiltonian systems
    • Long Y.M. Multiple solutions of perturbed superquadratic second order Hamiltonian systems. Trans. Amer. Math. Soc. 1989, 311:749-780.
    • (1989) Trans. Amer. Math. Soc. , vol.311 , pp. 749-780
    • Long, Y.M.1
  • 15
    • 0001630228 scopus 로고
    • Maslov-type index, degenerate critical points, and asymptotically linear Hamiltonian systems
    • Long Y.M. Maslov-type index, degenerate critical points, and asymptotically linear Hamiltonian systems. Sci. China Ser. A 1990, 33:1409-1419.
    • (1990) Sci. China Ser. A , vol.33 , pp. 1409-1419
    • Long, Y.M.1
  • 16
    • 0002034029 scopus 로고
    • Periodic solutions of perturbed superquadratic Hamiltonian systems
    • Long Y.M. Periodic solutions of perturbed superquadratic Hamiltonian systems. Ann. Sc. Norm. Super. Pisa Cl. Sci. (4) 1990, 17:35-77.
    • (1990) Ann. Sc. Norm. Super. Pisa Cl. Sci. (4) , vol.17 , pp. 35-77
    • Long, Y.M.1
  • 17
    • 51249179243 scopus 로고
    • Periodic solutions of superquadratic Hamiltonian systems with bounded forcing terms
    • Long Y.M. Periodic solutions of superquadratic Hamiltonian systems with bounded forcing terms. Math. Z. 1990, 203:453-467.
    • (1990) Math. Z. , vol.203 , pp. 453-467
    • Long, Y.M.1
  • 18
    • 0000407687 scopus 로고
    • Nonlinear oscillations for classical Hamiltonian systems with bi-even subquadratic potentials
    • Long Y.M. Nonlinear oscillations for classical Hamiltonian systems with bi-even subquadratic potentials. Nonlinear Anal. 1995, 24:1665-1671.
    • (1995) Nonlinear Anal. , vol.24 , pp. 1665-1671
    • Long, Y.M.1
  • 19
    • 48749138522 scopus 로고
    • Existence of infinitely many periodic solutions for a perturbed Hamiltonian system
    • Pisani R., Tucci M. Existence of infinitely many periodic solutions for a perturbed Hamiltonian system. Nonlinear Anal. 1984, 8:873-891.
    • (1984) Nonlinear Anal. , vol.8 , pp. 873-891
    • Pisani, R.1    Tucci, M.2
  • 20
    • 0001901435 scopus 로고
    • Minimax Methods in Critical Point Theory with Applications to Differential Equations
    • American Mathematical Society, Providence, RI
    • Rabinowitz P.H. Minimax Methods in Critical Point Theory with Applications to Differential Equations. CBMS Reg. Conf. Ser. Math. 1986, vol. 65. American Mathematical Society, Providence, RI.
    • (1986) CBMS Reg. Conf. Ser. Math. , vol.65
    • Rabinowitz, P.H.1
  • 21
    • 84980196930 scopus 로고
    • Periodic solutions of Hamiltonian systems
    • Rabinowitz P.H. Periodic solutions of Hamiltonian systems. Comm. Pure Appl. Math. 1978, 31:157-184.
    • (1978) Comm. Pure Appl. Math. , vol.31 , pp. 157-184
    • Rabinowitz, P.H.1
  • 22
    • 84980174431 scopus 로고
    • On subharmonic solutions of Hamiltonian systems
    • Rabinowitz P.H. On subharmonic solutions of Hamiltonian systems. Comm. Pure Appl. Math. 1980, 33:609-633.
    • (1980) Comm. Pure Appl. Math. , vol.33 , pp. 609-633
    • Rabinowitz, P.H.1
  • 23
    • 0002809786 scopus 로고
    • Periodic solutions of large norm of Hamiltonian systems
    • Rabinowitz P.H. Periodic solutions of large norm of Hamiltonian systems. J. Differential Equations 1983, 50:33-48.
    • (1983) J. Differential Equations , vol.50 , pp. 33-48
    • Rabinowitz, P.H.1
  • 24
    • 0008990673 scopus 로고
    • Elementary Introduction to the Theory of Pseudodifferential Operators
    • CRC Press, Boca Raton, FL
    • Saint Raymond X. Elementary Introduction to the Theory of Pseudodifferential Operators. Stud. Adv. Math. 1991, CRC Press, Boca Raton, FL.
    • (1991) Stud. Adv. Math.
    • Saint Raymond, X.1
  • 25
    • 0032061550 scopus 로고    scopus 로고
    • Existence and multiplicity of periodic solutions for nonautonomous second order systems
    • Tang C.L. Existence and multiplicity of periodic solutions for nonautonomous second order systems. Nonlinear Anal. 1998, 32:299-304.
    • (1998) Nonlinear Anal. , vol.32 , pp. 299-304
    • Tang, C.L.1
  • 26
    • 0037146386 scopus 로고    scopus 로고
    • Infinitely many solutions for Hamiltonian systems
    • Zou W., Li S. Infinitely many solutions for Hamiltonian systems. J. Differential Equations 2002, 186:141-164.
    • (2002) J. Differential Equations , vol.186 , pp. 141-164
    • Zou, W.1    Li, S.2
  • 27
    • 0035532310 scopus 로고    scopus 로고
    • Variant fountain theorems and their applications
    • Zou W. Variant fountain theorems and their applications. Manuscripta Math. 2001, 104:343-358.
    • (2001) Manuscripta Math. , vol.104 , pp. 343-358
    • Zou, W.1
  • 28
    • 0035372016 scopus 로고    scopus 로고
    • Multiple solutions for second-order Hamiltonian systems via computation of the critical groups
    • Zou W. Multiple solutions for second-order Hamiltonian systems via computation of the critical groups. Nonlinear Anal. 2001, 44:975-989.
    • (2001) Nonlinear Anal. , vol.44 , pp. 975-989
    • Zou, W.1

* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.