Geodesic
Iterative technique for a third-order three-point BVP with sign-changing Green's function
Electronic Journal of Differential Equations, Tome 2013 (2013).

Voir la notice de l'article provenant de la source Electronic Library of Mathematics

Summary: 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.
Classification : 34B10, 34B18
Keywords: boundary value problem, Green's function, positive solution, existence of solutions, iterative technique 
@article{EJDE_2013__2013__a148,
     author = {Sun, Jian-Ping and Zhao, Juan},
     title = {Iterative technique for a third-order three-point {BVP} with sign-changing {Green's} function},
     journal = {Electronic Journal of Differential Equations},
     publisher = {mathdoc},
     volume = {2013},
     year = {2013},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/EJDE_2013__2013__a148/}
}
TY  - JOUR
AU  - Sun, Jian-Ping
AU  - Zhao, Juan
TI  - Iterative technique for a third-order three-point BVP with sign-changing Green's function
JO  - Electronic Journal of Differential Equations
PY  - 2013
VL  - 2013
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/item/EJDE_2013__2013__a148/
LA  - en
ID  - EJDE_2013__2013__a148
ER  - 
%0 Journal Article
%A Sun, Jian-Ping
%A Zhao, Juan
%T Iterative technique for a third-order three-point BVP with sign-changing Green's function
%J Electronic Journal of Differential Equations
%D 2013
%V 2013
%I mathdoc
%U http://geodesic.mathdoc.fr/item/EJDE_2013__2013__a148/
%G en
%F EJDE_2013__2013__a148
Sun, Jian-Ping; Zhao, Juan. Iterative technique for a third-order three-point BVP with sign-changing Green's function. Electronic Journal of Differential Equations, Tome 2013 (2013). http://geodesic.mathdoc.fr/item/EJDE_2013__2013__a148/