- About this Journal ·
- Abstracting and Indexing ·
- Advance Access ·
- Aims and Scope ·
- Annual Issues ·
- Article Processing Charges ·
- Articles in Press ·
- Author Guidelines ·
- Bibliographic Information ·
- Citations to this Journal ·
- Contact Information ·
- Editorial Board ·
- Editorial Workflow ·
- Free eTOC Alerts ·
- Publication Ethics ·
- Reviewers Acknowledgment ·
- Submit a Manuscript ·
- Subscription Information ·
- Table of Contents
Abstract and Applied Analysis
Volume 2012 (2012), Article ID 532430, 19 pages
Multiple Solutions for Degenerate Elliptic Systems Near Resonance at Higher Eigenvalues
1School of Sciences, Guizhou Minzu University, Guiyang 550025, China
2School of Mathematics and Computer Science, Bijie University, Bijie 551700, China
Received 24 February 2012; Accepted 29 April 2012
Academic Editor: Shaoyong Lai
Copyright © 2012 Yu-Cheng An and Hong-Min Suo. 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.
- P. Drábek, A. Kufner, and F. Nicolosi, Quasilinear Elliptic Equations with Degenerations and Singularities, Walter de Gruyter & Co., Berlin, Germany, 1997.
- N. B. Zographopoulos, “On the principal eigenvalue of degenerate quasilinear elliptic systems,” Mathematische Nachrichten, vol. 281, no. 9, pp. 1351–1365, 2008.
- R. Dautray and J.-L. Lions, Mathematical Analysis and Numerical Methods for Science and Technology, vol. 1 of Physical Origins and Classical Methods, Springer, Berlin, Germany, 1990.
- N. I. Karachalios and N. B. Zographopoulos, “On the dynamics of a degenerate parabolic equation: global bifurcation of stationary states and convergence,” Calculus of Variations and Partial Differential Equations, vol. 25, no. 3, pp. 361–393, 2006.
- J. Mawhin and K. Schmitt, “Nonlinear eigenvalue problems with the parameter near resonance,” Annales Polonici Mathematici, vol. 51, pp. 241–248, 1990.
- T. F. Ma, M. Ramos, and L. Sanchez, “Multiple solutions for a class of nonlinear boundary value problem near resonance: a variational approach,” Nonlinear Analysis, vol. 30, no. 6, pp. 3301–3311, 1997.
- T. F. Ma and M. L. Pelicer, “Perturbations near resonance for the -Laplacian in ,” Abstract and Applied Analysis, vol. 7, no. 6, pp. 323–334, 2002.
- T. F. Ma and L. Sanchez, “Three solutions of a quasilinear elliptic problem near resonance,” Mathematica Slovaca, vol. 47, no. 4, pp. 451–457, 1997.
- Z.-Q. Ou and C.-L. Tang, “Existence and multiplicity results for some elliptic systems at resonance,” Nonlinear Analysis, vol. 71, no. 7-8, pp. 2660–2666, 2009.
- F. O. de Paiva and E. Massa, “Semilinear elliptic problems near resonance with a nonprincipal eigenvalue,” Journal of Mathematical Analysis and Applications, vol. 342, no. 1, pp. 638–650, 2008.
- H.-M. Suo and C.-L. Tang, “Multiplicity results for some elliptic systems near resonance with a nonprincipal eigenvalue,” Nonlinear Analysis, vol. 73, no. 7, pp. 1909–1920, 2010.
- D. G. de Figueiredo, “Positive solutions of semilinear elliptic problems,” in Differential Equations, São Paulo, 1981, vol. 957 of Lecture Notes in Mathematics, pp. 34–87, Springer, Berlin, Germany, 1982.
- A. Marino, A. M. Micheletti, and A. Pistoia, “A nonsymmetric asymptotically linear elliptic problem,” Topological Methods in Nonlinear Analysis, vol. 4, no. 2, pp. 289–339, 1994.
- D. G. de Figueiredo, Lectures on the Ekeland Variational Principle with Applications and Detours, vol. 81 of Tata Institute of Fundamental Research Lectures on Mathematics and Physics, Tata Institute of Fundamental Research, Bombay, India, 1989.
- P. H. 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.
- C.-L. Tang and X.-P. Wu, “Periodic solutions for second order systems with not uniformly coercive potential,” Journal of Mathematical Analysis and Applications, vol. 259, no. 2, pp. 386–397, 2001.