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Volumn 239, Issue 1, 2007, Pages 196-212

Periodic solutions of second order non-autonomous singular dynamical systems

Author keywords

Dynamical systems; Leray Schauder alternative principle; Non autonomous; Periodic solutions; Schauder's fixed point theorem; Strong singularity; Weak singularity

Indexed keywords


EID: 34250691602     PISSN: 00220396     EISSN: 10902732     Source Type: Journal    
DOI: 10.1016/j.jde.2007.05.007     Document Type: Article
Times cited : (150)

References (32)
  • 1
    • 34250729894 scopus 로고    scopus 로고
    • Non-collision periodic solutions of prescribed energy problem for a class of singular Hamiltonian systems
    • Adachi S. Non-collision periodic solutions of prescribed energy problem for a class of singular Hamiltonian systems. Topol. Methods Nonlinear Anal. 25 (2005) 275-296
    • (2005) Topol. Methods Nonlinear Anal. , vol.25 , pp. 275-296
    • Adachi, S.1
  • 3
    • 14844360218 scopus 로고    scopus 로고
    • Forced singular oscillators and the method of lower and upper solutions
    • Bonheure D., and De Coster C. Forced singular oscillators and the method of lower and upper solutions. Topol. Methods Nonlinear Anal. 22 (2003) 297-317
    • (2003) Topol. Methods Nonlinear Anal. , vol.22 , pp. 297-317
    • Bonheure, D.1    De Coster, C.2
  • 4
    • 33646394064 scopus 로고    scopus 로고
    • Multiplicity of positive solutions to second order differential equations
    • Chu J., Lin X., Jiang D., O'Regan D., and Agarwal P.R. Multiplicity of positive solutions to second order differential equations. Bull. Austral. Math. Soc. 73 (2006) 175-182
    • (2006) Bull. Austral. Math. Soc. , vol.73 , pp. 175-182
    • Chu, J.1    Lin, X.2    Jiang, D.3    O'Regan, D.4    Agarwal, P.R.5
  • 5
    • 34250774621 scopus 로고    scopus 로고
    • J. Chu, P.J. Torres, Applications of Schauder's fixed point theorem to singular differential equations, Bull. London Math. Soc., in press
  • 6
    • 84974027478 scopus 로고
    • T-periodic solutions for some second order differential equations with singularities
    • del Pino M., Manásevich R., and Montero A. T-periodic solutions for some second order differential equations with singularities. Proc. Roy. Soc. Edinburgh Sect. A 120 (1992) 231-243
    • (1992) Proc. Roy. Soc. Edinburgh Sect. A , vol.120 , pp. 231-243
    • del Pino, M.1    Manásevich, R.2    Montero, A.3
  • 7
    • 0001196155 scopus 로고
    • Infinitely many T-periodic solutions for a problem arising in nonlinear elasticity
    • del Pino M., and Manásevich R. Infinitely many T-periodic solutions for a problem arising in nonlinear elasticity. J. Differential Equations 103 (1993) 260-277
    • (1993) J. Differential Equations , vol.103 , pp. 260-277
    • del Pino, M.1    Manásevich, R.2
  • 8
    • 0842325119 scopus 로고    scopus 로고
    • On the existence of collisionless equivariant minimizers for the classical n-body problem
    • Ferrario D.L., and Terracini S. On the existence of collisionless equivariant minimizers for the classical n-body problem. Invent. Math. 155 (2004) 305-362
    • (2004) Invent. Math. , vol.155 , pp. 305-362
    • Ferrario, D.L.1    Terracini, S.2
  • 9
    • 21144470754 scopus 로고
    • Subharmonic solutions for some second order differential equations with singularities
    • Fonda A., Manásevich R., and Zanolin F. Subharmonic solutions for some second order differential equations with singularities. SIAM J. Math. Anal. 24 (1993) 1294-1311
    • (1993) SIAM J. Math. Anal. , vol.24 , pp. 1294-1311
    • Fonda, A.1    Manásevich, R.2    Zanolin, F.3
  • 10
    • 33750172329 scopus 로고    scopus 로고
    • Collisionless orbits of singular and nonsingular dynamical systems
    • Franco D., and Webb J.R.L. Collisionless orbits of singular and nonsingular dynamical systems. Discrete Contin. Dyn. Syst. 15 (2006) 747-757
    • (2006) Discrete Contin. Dyn. Syst. , vol.15 , pp. 747-757
    • Franco, D.1    Webb, J.R.L.2
  • 11
    • 34250700136 scopus 로고    scopus 로고
    • D. Franco, P.J. Torres, Periodic solutions of singular systems without the strong force condition, Proc. Amer. Math. Soc., in press
  • 12
    • 84967782996 scopus 로고
    • Conservative dynamical systems involving strong forces
    • Gordon W.B. Conservative dynamical systems involving strong forces. Trans. Amer. Math. Soc. 204 (1975) 113-135
    • (1975) Trans. Amer. Math. Soc. , vol.204 , pp. 113-135
    • Gordon, W.B.1
  • 13
    • 67651101560 scopus 로고
    • Periodic solution of some Liénard equations with singularities
    • Habets P., and Sanchez L. Periodic solution of some Liénard equations with singularities. Proc. Amer. Math. Soc. 109 (1990) 1135-1144
    • (1990) Proc. Amer. Math. Soc. , vol.109 , pp. 1135-1144
    • Habets, P.1    Sanchez, L.2
  • 14
    • 0242593196 scopus 로고    scopus 로고
    • Multiple positive solutions to superlinear periodic boundary value problems with repulsive singular forces
    • Jiang D., Chu J., O'Regan D., and Agarwal R.P. Multiple positive solutions to superlinear periodic boundary value problems with repulsive singular forces. J. Math. Anal. Appl. 286 (2003) 563-576
    • (2003) J. Math. Anal. Appl. , vol.286 , pp. 563-576
    • Jiang, D.1    Chu, J.2    O'Regan, D.3    Agarwal, R.P.4
  • 15
    • 14844350923 scopus 로고    scopus 로고
    • Multiplicity of positive periodic solutions to superlinear repulsive singular equations
    • Jiang D., Chu J., and Zhang M. Multiplicity of positive periodic solutions to superlinear repulsive singular equations. J. Differential Equations 211 (2005) 282-302
    • (2005) J. Differential Equations , vol.211 , pp. 282-302
    • Jiang, D.1    Chu, J.2    Zhang, M.3
  • 16
    • 84968467454 scopus 로고
    • On periodic solutions of nonlinear differential equations with singularities
    • Lazer A.C., and Solimini S. On periodic solutions of nonlinear differential equations with singularities. Proc. Amer. Math. Soc. 99 (1987) 109-114
    • (1987) Proc. Amer. Math. Soc. , vol.99 , pp. 109-114
    • Lazer, A.C.1    Solimini, S.2
  • 17
    • 34250718259 scopus 로고    scopus 로고
    • Twin positive periodic solutions of second order singular differential systems
    • Lin X., Jiang D., O'Regan D., and Agarwal R.P. Twin positive periodic solutions of second order singular differential systems. Topol. Methods Nonlinear Anal. 25 (2005) 263-273
    • (2005) Topol. Methods Nonlinear Anal. , vol.25 , pp. 263-273
    • Lin, X.1    Jiang, D.2    O'Regan, D.3    Agarwal, R.P.4
  • 19
    • 0242693642 scopus 로고
    • Sur les solutions périodiques et le priciple de moindre action
    • Poincaré H. Sur les solutions périodiques et le priciple de moindre action. C. R. Math. Acad. Sci. Paris 22 (1896) 915-918
    • (1896) C. R. Math. Acad. Sci. Paris , vol.22 , pp. 915-918
    • Poincaré, H.1
  • 20
    • 0035506592 scopus 로고    scopus 로고
    • Existence of nonnegative and nonpositive solutions for second order periodic boundary value problems
    • Rachunková I., Tvrdý M., and Vrkoč I. Existence of nonnegative and nonpositive solutions for second order periodic boundary value problems. J. Differential Equations 176 (2001) 445-469
    • (2001) J. Differential Equations , vol.176 , pp. 445-469
    • Rachunková, I.1    Tvrdý, M.2    Vrkoč, I.3
  • 21
    • 0004414959 scopus 로고
    • Noncollision periodic solutions to some singular dynamical systems with very weak forces
    • Ramos M., and Terracini S. Noncollision periodic solutions to some singular dynamical systems with very weak forces. J. Differential Equations 118 (1995) 121-152
    • (1995) J. Differential Equations , vol.118 , pp. 121-152
    • Ramos, M.1    Terracini, S.2
  • 22
    • 33645124842 scopus 로고    scopus 로고
    • Periodic non-autonomous second-order dynamical systems
    • Schechter M. Periodic non-autonomous second-order dynamical systems. J. Differential Equations 223 (2006) 290-302
    • (2006) J. Differential Equations , vol.223 , pp. 290-302
    • Schechter, M.1
  • 23
    • 0001177992 scopus 로고
    • On forced dynamical systems with a singularity of repulsive type
    • Solimini S. On forced dynamical systems with a singularity of repulsive type. Nonlinear Anal. 14 (1990) 489-500
    • (1990) Nonlinear Anal. , vol.14 , pp. 489-500
    • Solimini, S.1
  • 24
    • 84966248520 scopus 로고
    • A note on generalized solutions of singular Hamiltonian systems
    • Tanaka K. A note on generalized solutions of singular Hamiltonian systems. Proc. Amer. Math. Soc. 122 (1994) 275-284
    • (1994) Proc. Amer. Math. Soc. , vol.122 , pp. 275-284
    • Tanaka, K.1
  • 25
    • 38249007043 scopus 로고
    • Remarks on periodic orbits of dynamical systems with repulsive singularities
    • Terracini S. Remarks on periodic orbits of dynamical systems with repulsive singularities. J. Funct. Anal. 111 (1993) 213-238
    • (1993) J. Funct. Anal. , vol.111 , pp. 213-238
    • Terracini, S.1
  • 26
    • 0038702598 scopus 로고    scopus 로고
    • Existence of one-signed periodic solutions of some second-order differential equations via a Krasnoselskii fixed point theorem
    • Torres P.J. Existence of one-signed periodic solutions of some second-order differential equations via a Krasnoselskii fixed point theorem. J. Differential Equations 190 (2003) 643-662
    • (2003) J. Differential Equations , vol.190 , pp. 643-662
    • Torres, P.J.1
  • 27
    • 4944229622 scopus 로고    scopus 로고
    • Non-collision periodic solutions of forced dynamical systems with weak singularities
    • Torres P.J. Non-collision periodic solutions of forced dynamical systems with weak singularities. Discrete Contin. Dyn. Syst. 11 (2004) 693-698
    • (2004) Discrete Contin. Dyn. Syst. , vol.11 , pp. 693-698
    • Torres, P.J.1
  • 28
    • 33750163929 scopus 로고    scopus 로고
    • Weak singularities may help periodic solutions to exist
    • Torres P.J. Weak singularities may help periodic solutions to exist. J. Differential Equations 232 (2007) 277-284
    • (2007) J. Differential Equations , vol.232 , pp. 277-284
    • Torres, P.J.1
  • 29
    • 22444454256 scopus 로고    scopus 로고
    • Periodic solutions of damped differential systems with repulsive singular forces
    • Zhang M. Periodic solutions of damped differential systems with repulsive singular forces. Proc. Amer. Math. Soc. 127 (1999) 401-407
    • (1999) Proc. Amer. Math. Soc. , vol.127 , pp. 401-407
    • Zhang, M.1
  • 31
    • 33644588170 scopus 로고    scopus 로고
    • Periodic solutions of equations of Emarkov-Pinney type
    • Zhang M. Periodic solutions of equations of Emarkov-Pinney type. Adv. Nonlinear Stud. 6 (2006) 57-67
    • (2006) Adv. Nonlinear Stud. , vol.6 , pp. 57-67
    • Zhang, M.1
  • 32
    • 1042291018 scopus 로고    scopus 로고
    • Nonplanar and noncollision periodic solutions for N-body problems
    • Zhang S., and Zhou Q. Nonplanar and noncollision periodic solutions for N-body problems. Discrete Contin. Dyn. Syst. 10 (2004) 679-685
    • (2004) Discrete Contin. Dyn. Syst. , vol.10 , pp. 679-685
    • Zhang, S.1    Zhou, Q.2


* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.