Electron. J. Diff. Equ., Vol. 2013 (2013), No. 215, pp. 1-9.

Iterative technique for a third-order three-point BVP with sign-changing Green's function

Jian-Ping Sun, Juan Zhao

Abstract:
In this article, by applying iterative technique, we study the third-order three-point boundary value problem
$$\displaylines{ u'''(t)=f(t,u(t)),\quad t\in [0,1], \cr u'(0)=u''(\eta)=u(1)=0, }$$
where $f\in C([0,1]\times[0,+\infty),[0,+\infty))$ and $\eta\in[2-\sqrt{2},1)$. The emphasis is mainly that although the corresponding Green's function is sign-changing, the solution obtained is still positive. Moreover, our iterative scheme starts off with zero function, which implies that the iterative scheme is feasible. An example is also included to illustrate the main results.

Submitted July 5, 2013. Published September 30, 2013.
Math Subject Classifications: 34B10, 34B18.
Key Words: Boundary value problem; Green's function; positive solution; existence of solutions; iterative technique.

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Jian-Ping Sun
Department of Applied Mathematics
Lanzhou University of Technology,
Lanzhou, Gansu 730050, China
email: jpsun2012@163.com
Juan Zhao
Department of Applied Mathematics
Lanzhou University of Technology
Lanzhou, Gansu 730050, China
email: jzhao79@163.com

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