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Abstract and Applied Analysis
Volume 2013 (2013), Article ID 603703, 9 pages
The Method of Coupled Fixed Points and Coupled Quasisolutions When Working with ODE’s with Arguments of Bounded Variation
1Department of Mathematical Analysis, University of Santiago de Compostela, 15782 Santiago de Compostela, Spain
2Department of Specific Didactics, University of Burgos, 09001 Burgos, Spain
Received 14 May 2013; Revised 2 October 2013; Accepted 4 October 2013
Academic Editor: Marcia Federson
Copyright © 2013 Rubén Figueroa. 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. Figueroa and R. L. Pouso, “Coupled fixed points of multivalued operators and first-order ODEs with state-dependent deviating arguments,” Nonlinear Analysis: Theory, Methods & Applications, vol. 74, no. 18, pp. 6876–6889, 2011.
- A. Dyki and T. Jankowski, “Boundary value problems for ordinary differential equations with deviated arguments,” Journal of Optimization Theory and Applications, vol. 135, no. 2, pp. 257–269, 2007.
- R. Figueroa, “Discontinuous functional differential equations with delayed or advanced arguments,” Applied Mathematics and Computation, vol. 218, no. 19, pp. 9882–9889, 2012.
- T. Jankowski, “Advanced differential equations with nonlinear boundary conditions,” Journal of Mathematical Analysis and Applications, vol. 304, no. 2, pp. 490–503, 2005.
- T. M. Apostol, Mathematical Analysis, Addison-Wesley, Reading, Mass, USA, 2nd edition, 1974.
- E. Hewitt and K. Stromberg, Real and Abstract Analysis, Springer, New York, NY, USA, 3rd edition, 1975.
- S. Heikkilä and V. Lakshmikantham, Monotone Iterative Techniques for Discontinuous Nonlinear Differential Equations, vol. 181 of Monographs and Textbooks in Pure and Applied Mathematics, Marcel Dekker, New York, NY, USA, 1994.
- E. R. Hassan and W. Rzymowski, “Extremal solutions of a discontinuous scalar differential equation,” Nonlinear Analysis: Theory, Methods & Applications, vol. 37, no. 8, pp. 997–1017, 1999.
- R. L. Pouso, “Nonordered discontinuous upper and lower solutions for first-order ordinary differential equations,” Nonlinear Analysis: Theory, Methods & Applications, vol. 45, no. 4, pp. 391–406, 2001.
- R. L. Pouso, “Necessary conditions for solving initial value problems with infima of superfunctions,” Mathematical Inequalities & Applications, vol. 8, no. 4, pp. 633–641, 2005.