Ground state homoclinic orbits of superquadratic damped vibration systems

详细信息    查看全文

• 作者：Guanwei Chen (7)
  Xiaoming Zhao (8)
  
  7. School of Mathematics and Statistics ; Anyang Normal University ; Anyang ; Henan Province ; 455000 ; P.R. China
  8. Petrochina Pipeline Company ; Langfang ; Hebei Province ; 065000 ; P.R. China
  
• 关键词：damped vibration systems ; ground state homoclinic orbits ; superlinear ; variant weak linking theorem
• 刊名：Advances in Difference Equations
• 出版年：2014
• 出版时间：December 2014
• 年：2014
• 卷：2014
• 期：1
• 全文大小：347 KB
• 参考文献：1. Ambrosetti, A, Coti Zelati, V (1993) Multiple homoclinic orbits for a class of conservative systems. Rend. Semin. Mat. Univ. Padova 89: pp. 177-194
  2. Chen, G, Ma, S (2011) Periodic solutions for Hamiltonian systems without Ambrosetti-Rabinowitz condition and spectrum. J.脗聽Math. Anal. Appl 379: pp. 842-851 CrossRef
  3. Ding, Y (1995) Existence and multiplicity results for homoclinic solutions to a class of Hamiltonian systems. Nonlinear Anal 25: pp. 1095-1113 CrossRef
  4. Izydorek, M, Janczewska, J (2005) Homoclinic solutions for a class of second order Hamiltonian systems. J. Differ. Equ 219: pp. 375-389 CrossRef
  5. Kim, Y (2011) Existence of periodic solutions for planar Hamiltonian systems at resonance. J. Korean Math. Soc 48: pp. 1143-1152 CrossRef
  6. Mawhin, J, Willem, M (1989) Applied Mathematical Sciences 74. Critical Point Theory and Hamiltonian Systems. Springer, New York CrossRef
  7. Omana, W, Willem, M (1992) Homoclinic orbits for a class of Hamiltonian systems. Differ. Integral Equ 5: pp. 1115-1120
  8. Paturel, E (2001) Multiple homoclinic orbits for a class of Hamiltonian systems. Calc. Var. Partial Differ. Equ 12: pp. 117-143 CrossRef
  9. Rabinowitz, PH (1990) Homoclinic orbits for a class of Hamiltonian systems. Proc. R. Soc. Edinb., Sect. A 114: pp. 33-38 CrossRef
  10. Rabinowitz, PH, Tanaka, K (1991) Some results on connecting orbits for a class of Hamiltonian systems. Math. Z 206: pp. 473-499 CrossRef
  11. S茅r茅, E (1992) Existence of infinitely many homoclinic orbits in Hamiltonian systems. Math. Z 209: pp. 133-160 CrossRef
  12. Sun, J, Chen, H, Nieto, JJ (2011) Homoclinic solutions for a class of subquadratic second-order Hamiltonian systems. J. Math. Anal. Appl 373: pp. 20-29 CrossRef
  13. Tang, X, Xiao, L (2009) Homoclinic solutions for non-autonomous second-order Hamiltonian systems with a coercive potential. J. Math. Anal. Appl 351: pp. 586-594 CrossRef
  14. Wan, L, Tang, C (2011) Existence and multiplicity of homoclinic orbits for second order Hamiltonian systems without (AR) condition. Discrete Contin. Dyn. Syst., Ser. B 15: pp. 255-271
  15. Xiao, J, Nieto, JJ (2011) Variational approach to some damped Dirichlet nonlinear impulsive differential equations. J. Franklin Inst 348: pp. 369-377 CrossRef
  16. Zhang, P, Tang, C (2010) Infinitely many periodic solutions for nonautonomous sublinear second-order Hamiltonian systems. Abstr. Appl. Anal.
  17. Zhang, Q, Liu, C (2010) Infinitely many homoclinic solutions for second order Hamiltonian systems. Nonlinear Anal 72: pp. 894-903 CrossRef
  18. Chen, G (2013) Non-periodic damped vibration systems with sublinear terms at infinity: infinitely many homoclinic orbits. Nonlinear Anal 92: pp. 168-176 CrossRef
  19. Chen, G (2013) Non-periodic damped vibration systems with asymptotically quadratic terms at infinity: infinitely many homoclinic orbits. Abstr. Appl. Anal.
  20. Wu, X, Zhang, W (2011) Existence and multiplicity of homoclinic solutions for a class of damped vibration problems. Nonlinear Anal 74: pp. 4392-4398 CrossRef
  21. Zhang, Z, Yuan, R (2009) Homoclinic solutions for some second-order nonautonomous systems. Nonlinear Anal 71: pp. 5790-5798 CrossRef
  22. Zhu, W (2012) Existence of homoclinic solutions for a class of second order systems. Nonlinear Anal 75: pp. 2455-2463 CrossRef
  23. Schechter, M, Zou, W (2003) Weak linking theorems and Schr枚dinger equations with critical Sobolev exponent. ESAIM Control Optim. Calc. Var 9: pp. 601-619 CrossRef
  24. Costa, DG, Magalh茫es, CA (1994) A variational approach to subquadratic perturbations of elliptic systems. J. Differ. Equ 111: pp. 103-122 CrossRef
  25. Wang, J, Xu, J, Zhang, F (2011) Homoclinic orbits for a class of Hamiltonian systems with superquadratic or asymptotically quadratic potentials. Commun. Pure Appl. Anal 10: pp. 269-286 CrossRef
  26. Willem, M (1996) Minimax Theorems. Birkh盲user, Boston CrossRef
  
• 刊物主题：Difference and Functional Equations; Mathematics, general; Analysis; Functional Analysis; Ordinary Differential Equations; Partial Differential Equations;
• 出版者：Springer International Publishing
• ISSN：1687-1847

文摘

In the case where nonlinearities are superquadratic at infinity, we study the existence of ground state homoclinic orbits for damped vibration systems without periodic conditions by using variational methods. Here the (local) Ambrosetti-Rabinowitz superquadratic condition is replaced by a general superquadratic condition. MSC: 49J40, 70H05.