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Infinitely Many Fast Homoclinic Solutions for Some Second-Order Nonautonomous Systems

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We investigate the existence of infinitely many fast homoclinic solutions for a class of second-order nonautonomous systems. Our main tools are based on the variant fountain theorem. A criterion guaranteeing that the second-order system has infinitely many fast homoclinic solutions is obtained. Recent results from the literature are generalized and significantly improved.

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Author information

Correspondence to Liu Yang.

Additional information

Published in Ukrains’kyi Matematychnyi Zhurnal, Vol. 66, No. 3, pp. 404–414, March, 2014.

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Yang, L., Luo, L. & Luo, Z. Infinitely Many Fast Homoclinic Solutions for Some Second-Order Nonautonomous Systems. Ukr Math J 66, 454–466 (2014). https://doi.org/10.1007/s11253-014-0943-6

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Keywords

  • Hamiltonian System
  • Homoclinic Orbit
  • Weighted Sobolev Space
  • Homoclinic Solution
  • Positive Continuous Function