Third order problems with nonlocal conditions of integral type

详细信息    查看全文

• 作者：Abdelkader Boucherif (1)
  Sidi Mohamed Bouguima (2)
  Zehour Benbouziane (2)
  Nawal Al-Malki (3)
  
  1. Department of Mathematics and Statistics ; King Fahd University of Petroleum and Minerals ; P.O. Box 5046 ; Dhahran ; 31261 ; Saudi Arabia
  2. Department of Mathematics ; University of Tlemcen ; P.O. Box 119 ; Tlemcen ; 13000 ; Algeria
  3. Department of Mathematics ; Dammam University ; P.O. Box 838 ; Dammam ; Saudi Arabia
  
• 关键词：34B10 ; 34B11 ; 34B12 ; 34B13 ; 34B14 ; 34B15 ; third order differential equations ; integral boundary conditions ; a priori bound on solutions ; fixed point theorems ; lower and upper solutions ; iterative technique
• 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：1,220 KB
• 参考文献：1. Boucherif, A, Al-Malki, N (2007) Nonlinear three-point third order boundary value problems. Appl. Math. Comput. 190: pp. 1168-1177 CrossRef
  2. Minh贸s, FM (2008) On some third order nonlinear boundary value problems: existence, location and multiplicity results. J.聽Math. Anal. Appl. 339: pp. 1342-1353 CrossRef
  3. Grossinho, MR, Minh贸s, FM (2001) Existence results for some third order separated boundary value problems. Nonlinear Anal. 47: pp. 2407-2418 CrossRef
  4. Klokov, YA (2000) Upper and lower functions in boundary value problems for third-order ordinary differential equations. Differ. Equ. 36: pp. 1762-1769 CrossRef
  5. Boucherif, A, Bouguima, SM, Al-Malki, N, Benbouziane, ZN (2009) Third order differential equations with integral boundary conditions. Nonlinear Anal. 71: pp. e1736-e1743 CrossRef
  6. Benbouziane, ZN, Boucherif, A, Bouguima, SM (2004) Third order nonlocal multipoint boundary value problems. Dyn. Syst. Appl. 13: pp. 41-48
  7. Gray, M (2007) Uniqueness implies uniqueness for nonlocal boundary value problems for third order ordinary differential equations. Dyn. Syst. Appl. 16: pp. 277-284
  8. Wang, Y, Ge, W (2007) Existence of solutions for a third order differential equation with integral boundary conditions. Comput. Math. Appl. 53: pp. 144-154 CrossRef
  9. Graef, J, Kong, L, Minh贸s, F (2011) Higher order functional boundary value problems: existence and location results. Acta Sci. Math. 77: pp. 87-100
  10. Smart, DR (1974) Fixed Point Theorems. Cambridge University Press, Cambridge
  
• 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

We discuss the existence of solutions of nonlinear third order ordinary differential equations with integral boundary conditions. We provide sufficient conditions on the nonlinearity and the functions appearing in the boundary conditions that guarantee the existence of at least one solution to our problem. We rely on the method of lower and upper solutions to generate an iterative technique, which is not necessarily monotone.