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Abstract and Applied Analysis
Volume 2013 (2013), Article ID 138623, 9 pages
Heteroclinic Solutions for Nonautonomous EFK Equations
1School of Mathematics and Systems Science, Beijing University of Aeronautics and Astronautics, Beijing 100191, China
2School of Mathematical Sciences, Peking University, Beijing 100875, China
Received 30 August 2012; Accepted 12 February 2013
Academic Editor: Nikolaos Papageorgiou
Copyright © 2013 Y. L. Yeun. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
- L. A. Peletier and W. C. Troy, “Spatial patterns described by the extended Fisher-Kolmogorov (EFK) equation: kinks,” Differential and Integral Equations, vol. 8, no. 6, pp. 1279–1304, 1995.
- L. A. Peletier and W. C. Troy, “A topological shooting method and the existence of kinks of the extended Fisher-Kolmogorov equation,” Topological Methods in Nonlinear Analysis, vol. 6, no. 2, pp. 331–355, 1995.
- L. A. Peletier and W. C. Troy, “Chaotic spatial patterns described by the extended Fisher-Kolmogorov equation,” Journal of Differential Equations, vol. 129, no. 2, pp. 458–508, 1996.
- L. A. Peletier and W. C. Troy, “Spatial patterns described by the extended Fisher-Kolmogorov equation: periodic solutions,” SIAM Journal on Mathematical Analysis, vol. 28, no. 6, pp. 1317–1353, 1997.
- W. D. Kalies and R. C. A. M. VanderVorst, “Multitransition homoclinic and heteroclinic solutions of the extended Fisher-Kolmogorov equation,” Journal of Differential Equations, vol. 131, no. 2, pp. 209–228, 1996.
- W. D. Kalies, J. Kwapisz, and R. C. A. M. VanderVorst, “Homotopy classes for stable connections between Hamiltonian saddle-focus equilibria,” Communications in Mathematical Physics, vol. 193, no. 2, pp. 337–371, 1998.
- W. D. Kalies, J. Kwapisz, J. B. VandenBerg, and R. C. A. M. VanderVorst, “Homotopy classes for stable periodic and chaotic patterns in fourth-order Hamiltonian systems,” Communications in Mathematical Physics, vol. 214, no. 3, pp. 573–592, 2000.
- Y. Ruan, “Periodic and homoclinic solutions of a class of fourth order equations,” The Rocky Mountain Journal of Mathematics, vol. 41, no. 3, pp. 885–907, 2011.
- L. Yeun, “Heteroclinic solutions for fourth order equations of EFK type,” Forthcoming.
- D. Bonheure and L. Sanchez, “Heteroclinic orbits for some classes of second and fourth order differential equations,” in Handbook of Differential Equations: Ordinary Differential Equations, A. Canada, P. Drabek, and A. Fonda, Eds., vol. 3, chapter 2, pp. 103–202, Elsevier/North-Holland, Amsterdam, The Netherlands, 2006.
- P. H. Rabinowitz, “Periodic and heteroclinic orbits for a periodic Hamiltonian system,” Annales de l'Institut Henri Poincaré, Analyse Non Linéaire, vol. 6, no. 5, pp. 331–346, 1989.
- P. H. Rabinowitz, “Homoclinic and heteroclinic orbits for a class of Hamiltonian systems,” Calculus of Variations and Partial Differential Equations, vol. 1, no. 1, pp. 1–36, 1993.
- M. Izydorek and J. Janczewska, “Heteroclinic solutions for a class of the second order Hamiltonian systems,” Journal of Differential Equations, vol. 238, no. 2, pp. 381–393, 2007.
- Y. Ruan, “Notes on a class of one-dimensional Landau-Brazovsky models,” Archiv der Mathematik, vol. 93, no. 1, pp. 77–86, 2009.