Iterative technique for third-order differential equation with three-point nonlinear boundary value conditions

In this paper, we study the existence of extremal solutions for a nonlinear third-order differential equation with three-point nonlinear boundary value conditions. By means of the method of upper and lower solutions and different monotone iterative techniques, the sufficient conditions which guarantee the existence of extremal solutions are given. An example illustrates the main results.

[1]  Abdelkader Boucherif,et al.  Nonlinear three-point third-order boundary value problems , 2007, Appl. Math. Comput..

[2]  Weigao Ge,et al.  Existence of solutions for a class of third-order nonlinear boundary value problems , 2004 .

[3]  Mustafa Fahri Aktas,et al.  On the Lyapunov-type inequalities of a three-point boundary value problem for third order linear differential equations , 2015, Appl. Math. Lett..

[4]  Yongping Sun,et al.  Positive solutions for third-order three-point nonhomogeneous boundary value problems , 2009, Appl. Math. Lett..

[5]  Eva Rovderová.  Third-order boundary-value problem with nonlinear boundary conditions , 1995 .

[6]  Christopher S. Goodrich,et al.  Positive solutions to boundary value problems with nonlinear boundary conditions , 2012 .

[7]  MULTIPLE POSITIVE SOLUTIONS FOR NONLINEAR THIRD-ORDER THREE-POINT BOUNDARY-VALUE PROBLEMS , 2007 .

[8]  Weigao Ge,et al.  Singular perturbations for third-order nonlinear multi-point boundary value problem , 2005 .

[9]  Hanying Feng,et al.  Eigenvalue for a singular third-order three-point boundary value problem , 2013, Appl. Math. Comput..

[10]  Zhongli Wei.  Some necessary and sufficient conditions for existence of positive solutions for third order singular super-linear multi-point boundary value problems , 2014, Journal of Applied Mathematics and Computing.

[11]  Jian-Ping Sun,et al.  Existence of positive solutions for nonlinear third-order three-point boundary value problems☆ , 2008 .

[12]  John R. Graef,et al.  Positive solutions of a third order nonlocal boundary value problem , 2007 .

[13]  J. Webb,et al.  Third order boundary value problems with nonlocal boundary conditions , 2009 .

[14]  Douglas R. Anderson,et al.  Green's function for a third-order generalized right focal problem , 2003 .