- About this Journal
- Abstracting and Indexing
- 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 2013 (2013), Article ID 406350, 8 pages
Nodal Solutions of the p-Laplacian with Sign-Changing Weight
1Department of Mathematics, Northwest Normal University, Lanzhou 730070, China
2Department of Mathematics, Qinghai University for Nationalities, Xining 810007, China
Received 27 July 2013; Accepted 16 October 2013
Academic Editor: Paul Eloe
Copyright © 2013 Ruyun Ma et al. 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.
- R. Ma and B. Thompson, “Nodal solutions for nonlinear eigenvalue problems,” Nonlinear Analysis: Theory, Methods & Applications, vol. 59, no. 5, pp. 707–718, 2004.
- P. H. Rabinowitz, “Nonlinear Sturm-Liouville problems for second order ordinary differential equations,” Communications on Pure and Applied Mathematics, vol. 23, pp. 939–961, 1970.
- P. H. Rabinowitz, “Some global results for nonlinear eigenvalue problems,” Journal of Functional Analysis, vol. 7, pp. 487–513, 1971.
- R. Ma and X. Han, “Existence of nodal solutions of a nonlinear eigenvalue problem with indefinite weight function,” Nonlinear Analysis: Theory, Methods & Applications, vol. 71, no. 5-6, pp. 2119–2125, 2009.
- Y. Cui, J. Sun, and Y. Zou, “Global bifurcation and multiple results for Sturm-Liouville problems,” Journal of Computational and Applied Mathematics, vol. 235, no. 8, pp. 2185–2192, 2011.
- R. Ma and D. O'Regan, “Nodal solutions for second-order -point boundary value problems with nonlinearities across several eigenvalues,” Nonlinear Analysis: Theory, Methods & Applications, vol. 64, no. 7, pp. 1562–1577, 2006.
- B. P. Rynne, “Global bifurcation for th-order boundary value problems and infinitely many solutions of superlinear problems,” Journal of Differential Equations, vol. 188, no. 2, pp. 461–472, 2003.
- R. Ma, “Bifurcation from infinity and multiple solutions for periodic boundary value problems,” Nonlinear Analysis: Theory, Methods & Applications, vol. 42, no. 1, pp. 27–39, 2000.
- Y. Liu and D. O'Regan, “Multiplicity results using bifurcation techniques for a class of boundary value problems of impulsive differential equations,” Communications in Nonlinear Science and Numerical Simulation, vol. 16, no. 4, pp. 1769–1775, 2011.
- J. Henderson and H. Wang, “Positive solutions for nonlinear eigenvalue problems,” Journal of Mathematical Analysis and Applications, vol. 208, no. 1, pp. 252–259, 1997.
- W. H. Fleming, “A selection-migration model in population genetics,” Journal of Mathematical Biology, vol. 2, no. 3, pp. 219–233, 1975.
- M. del Pino, M. Elgueta, and R. Manásevich, “A homotopic deformation along of a Leray-Schauder degree result and existence for , , ,” Journal of Differential Equations, vol. 80, no. 1, pp. 1–13, 1989.
- I. Peral, “Multiplicity of solutions for the p-Laplacian,” ICTP SMR 990/1, 1997.
- M. A. del Pino and R. F. Manásevich, “Global bifurcation from the eigenvalues of the -Laplacian,” Journal of Differential Equations, vol. 92, no. 2, pp. 226–251, 1991.
- Y.-H. Lee and I. Sim, “Global bifurcation phenomena for singular one-dimensional -Laplacian,” Journal of Differential Equations, vol. 229, no. 1, pp. 229–256, 2006.
- P. Drábek and Y. X. Huang, “Bifurcation problems for the -Laplacian in ,” Transactions of the American Mathematical Society, vol. 349, no. 1, pp. 171–188, 1997.
- K. Schmitt and R. Thompson, Nonlinear Analysis and Differential Equations: An Introduction, University of Utah Lecture Notes, University of Utah Press, Salt Lake City, Utah, USA, 2004.
- A. Anane, O. Chakrone, and M. Moussa, “Spectrum of one dimensional -Laplacian operator with indefinite weight,” Electronic Journal of Qualitative Theory of Differential Equations, vol. 17, pp. 1–11, 2002.
- G. Meng, P. Yan, and M. Zhang, “Spectrum of one-dimensional -Laplacian with an indefinite integrable weight,” Mediterranean Journal of Mathematics, vol. 7, no. 2, pp. 225–248, 2010.
- K. Deimling, Nonlinear Functional Analysis, Springer, New-York, NY, USA, 1987.
- H. Brezis, Analyse Fonctionnelle: Theéorie et Applications, Masson, Paris, France, 1983.