- About this Journal ·
- Abstracting and Indexing ·
- Aims and Scope ·
- Annual Issues ·
- Article Processing Charges ·
- Author Guidelines ·
- Bibliographic Information ·
- Citations to this Journal ·
- Contact Information ·
- Editorial Board ·
- Editorial Workflow ·
- Free eTOC Alerts ·
- Publication Ethics ·
- Recently Accepted Articles ·
- Reviewers Acknowledgment ·
- Submit a Manuscript ·
- Subscription Information ·
- Table of Contents
Abstract and Applied Analysis
Volume 2012 (2012), Article ID 703596, 15 pages
Existence and Multiplicity Results of Homoclinic Solutions for the DNLS Equations with Unbounded Potentials
1School of Mathematics and Information Science, Guangzhou University, Guangdong, Guangzhou 510006, China
2Key Laboratory of Mathematics and Interdisciplinary Sciences of Guangdong Higher Education Institutes, Guangzhou University, Guangdong, Guangzhou 510006, China
Received 25 July 2012; Accepted 9 September 2012
Academic Editor: Wenming Zou
Copyright © 2012 Defang Ma and Zhan Zhou. 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.
- G. Teschl, Jacobi Operators and Completely Integrable Nonlinear Lattices, vol. 72 of Mathematical Surveys and Monographs, American Mathematical Society, Providence, RI, USA, 2000.
- S. Flach and A. Gorbach, “Discrete breakers-Advances in theory and applications,” Physics Reports, vol. 467, pp. 1–116, 2008.
- S. Flach and C. R. Willis, “Discrete breathers,” Physics Reports, vol. 295, no. 5, pp. 181–264, 1998.
- D. Hennig and G. P. Tsironis, “Wave transmission in nonlinear lattices,” Physics Reports, vol. 307, no. 5-6, pp. 333–432, 1999.
- G. Chen and S. Ma, “Discrete nonlinear Schrödinger equations with superlinear nonlinearities,” Applied Mathematics and Computation, vol. 218, no. 9, pp. 5496–5507, 2012.
- A. Pankov, “Gap solitons in periodic discrete nonlinear Schrödinger equations,” Nonlinearity, vol. 19, no. 1, pp. 27–40, 2006.
- A. Pankov, “Standing waves for discrete non-linear Schrödinger equations: sign-changing nonlinearities,” Applicable Analysis. In press.
- G. Zhang and A. Pankov, “Standing wave solutions of the discrete non-linear Schrödinger equations with unbounded potentials—II,” Applicable Analysis, vol. 89, no. 9, pp. 1541–1557, 2010.
- Z. Zhou, J. Yu, and Y. Chen, “Homoclinic solutions in periodic difference equations with saturable nonlinearity,” Science China Mathematics, vol. 54, no. 1, pp. 83–93, 2011.
- A. Pankov, “Gap solitons in periodic discrete nonlinear Schrödinger equations—II. A generalized Nehari manifold approach,” Discrete and Continuous Dynamical Systems. Series A, vol. 19, no. 2, pp. 419–430, 2007.
- A. Pankov, “Gap solitons in periodic discrete nonlinear Schrödinger equations with saturable nonlinearities,” Journal of Mathematical Analysis and Applications, vol. 371, no. 1, pp. 254–265, 2010.
- A. Pankov and V. Rothos, “Periodic and decaying solutions in discrete nonlinear Schrödinger with saturable nonlinearity,” Proceedings of The Royal Society of London. Series A, vol. 464, no. 2100, pp. 3219–3236, 2008.
- Z. Zhou and J. Yu, “On the existence of homoclinic solutions of a class of discrete nonlinear periodic systems,” Journal of Differential Equations, vol. 249, no. 5, pp. 1199–1212, 2010.
- Z. Zhou, J. Yu, and Y. Chen, “On the existence of gap solitons in a periodic discrete nonlinear Schrödinger equation with saturable nonlinearity,” Nonlinearity, vol. 23, no. 7, pp. 1727–1740, 2010.
- A. Pankov and G. Zhang, “Standing wave solutions for discrete nonlinear Schrödinger equations with unbounded potentials and saturable nonlinearity,” Journal of Mathematical Sciences, vol. 177, no. 1, pp. 71–82, 2011.
- G. Zhang and A. Pankov, “Standing waves of the discrete nonlinear Schrödinger equations with growing potentials,” Communications in Mathematical Analysis, vol. 5, no. 2, pp. 38–49, 2008.
- G. Zhang, “Breather solutions of the discrete nonlinear Schrödinger equations with unbounded potentials,” Journal of Mathematical Physics, vol. 50, no. 1, pp. 1–12, 2009.
- G. Zhang and F. Liu, “Existence of breather solutions of the DNLS equations with unbounded potentials,” Nonlinear Analysis. Theory, Methods & Applications, vol. 71, no. 12, pp. e786–e792, 2009.
- Y. Ding and C. Lee, “Multiple solutions of Schrödinger equations with indefinite linear part and super or asymptotically linear terms,” Journal of Differential Equations, vol. 222, no. 1, pp. 137–163, 2006.
- Q. Li, H. Su, and Z. Wei, “Existence of infinitely many large solutions for the nonlinear Schrödinger-Maxwell equations,” Nonlinear Analysis. Theory, Methods & Applications, vol. 72, no. 11, pp. 4264–4270, 2010.
- D. S. Moschetto, “Existence and multiplicity results for a nonlinear stationary Schrödinger equation,” Annales Polonici Mathematici, vol. 99, no. 1, pp. 39–43, 2010.
- M.-H. Yang and Z.-Q. Han, “Existence and multiplicity results for the nonlinear Schrödinger-Poisson systems,” Nonlinear Analysis. Real World Applications, vol. 13, no. 3, pp. 1093–1101, 2012.
- M. Willem, Minimax Theorems, Birkhäuser, Boston, Mass, USA, 1996.
- P. Rabinowitz, “Minimax methods in critical point theory with applications to differential equations,” vol. 65 of CBMS Regional Conference Series in Mathematics, American Mathematical Society, Providence, RI, USA, 1986.
- T. Bartsch, “Infinitely many solutions of a symmetric Dirichlet problem,” Nonlinear Analysis. Theory, Methods & Applications, vol. 20, no. 10, pp. 1205–1216, 1993.
- W. Zou, “Variant fountain theorems and their applications,” Manuscripta Mathematica, vol. 104, no. 3, pp. 343–358, 2001.