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Periodic solutions for nonautonomous second
order systems with sublinear nonlinearity


Author: Chun-Lei Tang
Journal: Proc. Amer. Math. Soc. 126 (1998), 3263-3270
MSC (1991): Primary 34C25, 58E50
MathSciNet review: 1476396
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Abstract: The existence and multiplicity of periodic solutions are obtained for nonautonomous second order systems with sublinear nonlinearity by using the least action principle and the minimax methods.


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  • 1. Haïm Brezis and Louis Nirenberg, Remarks on finding critical points, Comm. Pure Appl. Math. 44 (1991), no. 8-9, 939–963. MR 1127041, 10.1002/cpa.3160440808
  • 2. Yi Ming Long, Nonlinear oscillations for classical Hamiltonian systems with bi-even subquadratic potentials, Nonlinear Anal. 24 (1995), no. 12, 1665–1671. MR 1330641, 10.1016/0362-546X(94)00227-9
  • 3. Jean Mawhin and Michel Willem, Critical point theory and Hamiltonian systems, Applied Mathematical Sciences, vol. 74, Springer-Verlag, New York, 1989. MR 982267
  • 4. Paul H. Rabinowitz, Minimax methods in critical point theory with applications to differential equations, CBMS Regional Conference Series in Mathematics, vol. 65, Published for the Conference Board of the Mathematical Sciences, Washington, DC; by the American Mathematical Society, Providence, RI, 1986. MR 845785
  • 5. Chunlei Tang, Periodic solutions of non-autonomous second order systems with 𝛾-quasisubadditive potential, J. Math. Anal. Appl. 189 (1995), no. 3, 671–675. MR 1312546, 10.1006/jmaa.1995.1044
  • 6. C. L. Tang, Existence and multiplicity of periodic solutions for nonautonomous second order systems, Nonl. Anal. TMA, to appear.

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Additional Information

Chun-Lei Tang
Affiliation: Department of Mathematics, Southwest Normal University, Chongqing 400715, People’s Republic of China
Email: tangcl@swnu.edu.cn

DOI: http://dx.doi.org/10.1090/S0002-9939-98-04706-6
Keywords: Coercive, the (PS) condition, Sobolev's inequality, Wirtinger's inequality, the least action principle, the Saddle Point Theorem, periodic solution
Received by editor(s): March 18, 1997
Communicated by: Jeffrey B. Rauch
Article copyright: © Copyright 1998 American Mathematical Society