Upper and lower solutions method for fuzzy differential equations

• Autores: Juan José Nieto Roig , Rosana Rodríguez López
• Localización: SeMA Journal: Boletín de la Sociedad Española de Matemática Aplicada, ISSN-e 2254-3902, ISSN 2254-3902, Nº. 51, 2010, págs. 125-132
• Idioma: inglés
• DOI: 10.1007/bf03322563
• Texto completo no disponible (Saber más ...)
• Referencias bibliográficas
  • S. Abbasbandy, J.J. Nieto, M. Alavi, Tuning of reachable set in one dimensional fuzzy differential inclusions. Chaos Solitons Fractals, 26...
  • B. Bede, S.G. Gal, Generalizations of the differentiability of fuzzy-number-valued functions with applications to fuzzy differential equations....
  • B. Bede, I.J. Rudas, A. L. Bencsik, First order linear fuzzy differential equations under generalized differentiability. Inform. Sci., 177...
  • T. G. Bhaskar, V. Lakshmikantham, V. Devi, Revisiting fuzzy differential equations. Nonlinear Anal., 58 (2004), p. 351–358. DOI: 10.1016/j.na.2004.05.007
  • P. Diamond, Brief note on the variation of constants formula for fuzzy differential equations. Fuzzy Sets and Systems, 129 (2002), p. 65–71....
  • P. Diamond, P.E. Kloeden, Metric Spaces of Fuzzy Sets: Theory and Applications. World Scientific, Singapore 1994. DOI: 10.1142/2326
  • D. Dubois, H. Prade, Fuzzy Sets and Systems: Theory and Applications. Academic Press, New York 1980.
  • D. Dubois et al. (ed.) On boundary value problems for fuzzy differential equations. Soft Methods for Handling Variability and Imprecision,...
  • E. Hüllermeier, Numerical methods for fuzzy initial value problems. Internat. J. Uncertain. Fuzziness Knowledge-Based Syst., 7 (1999), p....
  • O. Kaleva, Fuzzy differential equations. Fuzzy Sets and Systems, 24 (1987), p. 301–317. DOI: 10.1016/0165-0114(87)90029-7
  • O. Kaleva, The Cauchy problem for fuzzy differential equations. Fuzzy Sets and Systems, 35 (1990), p. 389–396. DOI: 10.1016/0165-0114(90)90010-4
  • G. S. Ladde, V. Lakshmikantham, A. S. Vatsala, Monotone Iterative Techniques for Nonlinear Differential Equations. Pitman, Boston 1985.
  • V. Lakshmikantham, R.N. Mohapatra, Theory of Fuzzy Differential Equations and In- clusions. Taylor & Francis, London 2003. DOI: 10.1201/9780203011386
  • J.J. Nieto, R. Rodríguez-López, Contractive mapping theorems in partially ordered sets and applications to ordinary differential equations....
  • J.J. Nieto, R. Rodríguez-López, Bounded solutions for fuzzy differential and integral equations. Chaos Solitons Fractals, 27 (2006), 5, p....
  • J.J. Nieto, R. Rodríguez-López, Applications of contractive-like mapping principles to fuzzy and fuzzy differential equations. Rev Mat Complut,...
  • J.J. Nieto, R. Rodríguez-López, Existence and uniqueness of fixed point in partially ordered sets and applications to ordinary differential...
  • J. J. Nieto, R. Rodríguez-López, Complete Lattices in Fuzzy Real Line. The Journal of Fuzzy Mathematics, 17 (2009), 3, p. 745–762.
  • J.J. Nieto, R. Rodríguez-López, Existence and uniqueness results for fuzzy differential equations subject to boundary value conditions. In...
  • J.J. Nieto, R. Rodríguez-López, D. Franco, Linear first-order fuzzy differential equations. Internat. J. Uncertain. Fuzziness Knowledge-Based...
  • M. L. Puri, D. A. Ralescu, Differentials of fuzzy functions. J. Math. Anal. Appl., 91 (1983), p. 552–558. DOI: 10.1016/0022-247X(83)90169-5
  • A. C. M. Ran, M. C. B. Reurings, A fixed point theorem in partially ordered sets and some applications to matrix equations. Proc. Amer. Math....
  • R. Rodríguez-López, Periodic boundary value problems for impulsive fuzzy differential equations. Fuzzy Sets and Systems, 159 (2008), p. 1384–1409....
  • R. Rodríguez-López, Comparison results for fuzzy differential equations. Inform Sci., 178 (2008), p. 1756–1779. DOI: 10.1016/j.ins.2007.10.011
  • R. Rodríguez-López, Monotone method for fuzzy differential equations. Fuzzy Sets and Systems, 159 (2008), p. 2047–2076. DOI: 10.1016/j.fss.2007.12.020
  • S. Seikkala, On the fuzzy initial value problem. Fuzzy Sets and Systems, 24 (1987), 3, p. 319–330. DOI: 10.1016/0165-0114(87)90030-3
  • L. Stefanini, L. Sorini, M. L. Guerra, Parametric representation of fuzzy numbers and application to fuzzy calculus. Fuzzy Sets and Systems,...
  • A. Tarski, A lattice-theoretical fixpoint theorem and its applications. Pacific J. Math., 5 (1955), p. 285–309. DOI: 10.2140/pjm.1955.5.285
  • D. Vorobiev, S. Seikkala, Towards the theory of fuzzy differential equations. Fuzzy Sets and Systems, 125 (2002), 2, p. 231–237. DOI: 10.1016/S0165-0114(00)00131-7