Generalized monotone iterative method for nonlinear boundary value problems with causal operators

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• 作者：Wen-Li Wang (1)
  Jing-Feng Tian (2)
  
  1. Department of Information Engineering ; China University of Geosciences Great Wall College ; Baoding ; Hebei Province ; 071000 ; P.R. China
  2. College of Science and Technology ; North China Electric Power University ; Baoding ; Hebei Province ; 071051 ; P.R. China
  
• 关键词：34B15 ; 39B12 ; generalized monotone iterative method ; nonlinear boundary value problem ; upper and lower solutions ; causal operator
• 刊名：Boundary Value Problems
• 出版年：2014
• 出版时间：December 2014
• 年：2014
• 卷：2014
• 期：1
• 全文大小：1,223 KB
• 参考文献：1. Ladde, GS, Lakshmikantham, V, Vatsala, AS (1985) Monotone Iterative Techniques for Nonlinear Differential Equations. Pitman, London
  2. Agarwal, RP, Benchohra, N, Hamani, S (2010) A survey on existing results for boundary value problems of nonlinear fractional differential equations and inclusions. Acta Appl. Math. 109: pp. 973-1033 CrossRef
  3. Agarwal, RP, Franco, D, O鈥橰egan, D (2005) Singular boundary value problems for first and second order impulsive differential equations. Aequ. Math. 69: pp. 83-96 CrossRef
  4. Al-Refai, M, Ali Hajji, M (2011) Monotone iterative sequences for nonlinear boundary value problems of fractional order. Nonlinear Anal. 74: pp. 3531-3539 CrossRef
  5. Benchohra, M, Hamani, S (2009) The method of upper and lower solutions and impulsive fractional differential inclusions. Nonlinear Anal. Hybrid Syst. 3: pp. 433-440 CrossRef
  6. Bhaskar, TG, McRae, FA (2002) Monotone iterative techniques for nonlinear problems involving the difference of two monotone functions. Appl. Math. Comput. 133: pp. 187-192 CrossRef
  7. Cabada, A, Grossinhob, M, Minhosc, F (2005) Extremal solutions for third-order nonlinear problems with upper and lower solutions in reversed order. Nonlinear Anal. 62: pp. 1109-1121 CrossRef
  8. Corduneanu, C (2002) Functional Equations with Causal Operators Stability, and Control. Taylor & Francis, London CrossRef
  9. Cui, Y, Zou, Y (2013) Monotone iterative method for differential systems with coupled integral boundary value problems. Bound. Value Probl. 2013: CrossRef
  10. Franco, D, Nieto, JJ, O鈥橰egan, D (2004) Existence of solutions for first order differential equations with nonlinear boundary conditions. Appl. Math. Comput. 153: pp. 793-802 CrossRef
  11. Wang, W, Yang, X, Shen, J (2009) Boundary value problems involving upper and lower solutions in reverse order. J. Comput. Appl. Math. 230: pp. 1-7 CrossRef
  12. West, IH, Vatsala, AS (2004) Generalized monotone iterative method for initial value problems. Appl. Math. Lett. 17: pp. 1231-1237 CrossRef
  13. Lakshmikantham, V, Leela, S, Drici, Z, McRae, FA (2009) Theory of Causal Differential Equations. World Scientific, Singapore
  14. Drici, D, McRae, FA, Devi, JV (2006) Monotone iterative technique for periodic boundary value problems with causal operators. Nonlinear Anal. 64: pp. 1271-1277 CrossRef
  15. Li, Y, Sun, S, Yang, D, Han, Z (2013) Three-point boundary value problems of fractional functional differential equations with delay. Bound. Value Probl. 2013: CrossRef
  
• 刊物主题：Difference and Functional Equations; Ordinary Differential Equations; Partial Differential Equations; Analysis; Approximations and Expansions; Mathematics, general;
• 出版者：Springer International Publishing
• ISSN：1687-2770

文摘

This paper discusses nonlinear boundary value problems for causal differential equations where the right-hand side is the sum of two monotone functions. We develop the monotone iterative technique and establish the existence results of the extremal solutions. The results obtained include several special cases and extend previous results; two examples satisfying the assumptions are also presented.