Involve: A Journal of Mathematics

  • Involve
  • Volume 1, Number 1 (2008), 1-7.

Five-point boundary value problems for $n$-th order differential equations by solution matching

Johnny Henderson, John Ehrke, and Curtis Kunkel

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For the ordinary differential equation

y ( n ) = f ( x , y , y , y , , y ( n 1 ) ) , n 3 ,

solutions of three-point boundary value problems on [a,b] are matched with solutions of three-point boundary value problems on [b,c] to obtain solutions satisfying five-point boundary conditions on [a,c].

Article information

Involve, Volume 1, Number 1 (2008), 1-7.

Received: 2 April 2007
Accepted: 27 October 2007
First available in Project Euclid: 20 December 2017

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Digital Object Identifier

Mathematical Reviews number (MathSciNet)

Zentralblatt MATH identifier

Primary: 34B15: Nonlinear boundary value problems
Secondary: 34B10: Nonlocal and multipoint boundary value problems

boundary value problem ordinary differential equation solution matching


Henderson, Johnny; Ehrke, John; Kunkel, Curtis. Five-point boundary value problems for $n$-th order differential equations by solution matching. Involve 1 (2008), no. 1, 1--7. doi:10.2140/involve.2008.1.1.

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  • C. Bai and J. Fang, “Existence of multiple positive solutions for nonlinear $m$-point boundary value problems”, J. Math. Anal. Appl. 281:1 (2003), 76–85.
  • P. B. Bailey, L. F. Shampine, and P. E. Waltman, Nonlinear two point boundary value problems, Mathematics in Science and Engineering, Vol. 44, Academic Press, New York, 1968.
  • D. Barr and P. Miletta, “An existence and uniqueness criterion for solutions of boundary value problems”, J. Differential Equations 16:3 (1974), 460–471.
  • D. Barr and T. Sherman, “Existence and uniqueness of solutions of three-point boundary value problems”, J. Differential Equations 13 (1973), 197–212.
  • K. M. Das and B. S. Lalli, “Boundary value problems for $y\sp{\prime\prime\prime}\!=\!f(x,y,y\sp{\prime},\,y\sp{\prime\prime})$”, J. Math. Anal. Appl. 81:2 (1981), 300–307.
  • M. Eggensperger, E. R. Kaufmann, and N. Kosmatov, “Solution matching for a three-point boundary-value problem on a time scale”, Electron. J. Differential Equations (2004), No. 91, 7 pp. (electronic).
  • C. P. Gupta, “A nonlocal multipoint boundary-value problem at resonance”, pp. 253–259 in Advances in nonlinear dynamics, Stability Control Theory Methods Appl. 5, Gordon and Breach, Amsterdam, 1997.
  • C. P. Gupta and S. I. Trofimchuk, “Solvability of a multi-point boundary value problem and related a priori estimates”, Canad. Appl. Math. Quart. 6:1 (1998), 45–60. Geoffrey J. Butler Memorial Conference in Differential Equations and Mathematical Biology (Edmonton, AB, 1996).
  • J. Henderson, “Three-point boundary value problems for ordinary differential equations by matching solutions”, Nonlinear Anal. 7:4 (1983), 411–417.
  • J. Henderson and K. R. Prasad, “Existence and uniqueness of solutions of three-point boundary value problems on time scales by solution matching”, Nonlinear Stud. 8:1 (2001), 1–12.
  • J. Henderson and C. C. Tisdale, “Five-point boundary value problems for third-order differential equations by solution matching”, Math. Comput. Modelling 42:1-2 (2005), 133–137.
  • G. Infante, “Positive solutions of some three-point boundary value problems via fixed point index for weakly inward $A$-proper maps”, Fixed Point Theory Appl. 2005:2 (2005), 177–184.
  • R. Ma, “Existence theorems for a second order three-point boundary value problem”, J. Math. Anal. Appl. 212:2 (1997), 430–442.
  • R. Ma, “Existence of positive solutions for second order $m$-point boundary value problems”, Ann. Polon. Math. 79:3 (2002), 265–276.
  • V. R. G. Moorti and J. B. Garner, “Existence-uniqueness theorems for three-point boundary value problems for $n$th-order nonlinear differential equations”, J. Differential Equations 29:2 (1978), 205–213.
  • D. R. K. S. Rao, K. N. Murthy, and A. S. Rao, “Three-point boundary value problems associated with third order differential equations”, Nonlinear Anal. 5:6 (1981), 669–673.
  • J. R. L. Webb, “Optimal constants in a nonlocal boundary value problem”, Nonlinear Anal. 63:5-7 (2005), 672–685.