Geodesic
Uniqueness and parameter dependence of solutions of fourth-order four-point nonhomogeneous BVPs
Electronic Journal of Differential Equations, Tome 2010 (2010).

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

Summary: In this article, we investigate the fourth-order four-point nonhomogeneous Sturm-Liouville boundary-value problem $$\displaylines{ u^{(4)}(t)=f(t,u(t)),\quad t\in [0,1], \cr \alpha u(0)-\beta u'(0)=\gamma u(1)+\delta u'(1)=0, \cr au''(\xi _1)-bu'''(\xi _1)=-\lambda ,\quad cu''(\xi _2)+du'''(\xi _2)=-\mu , }$$ where $0\leq \xi _1\xi _2\leq 1$ and $\lambda$ and $\mu $ are nonnegative parameters. We obtain sufficient conditions for the existence and uniqueness of positive solutions. The dependence of the solution on the parameters $\lambda$ and $\mu $ is also studied.
Classification : 34B08, 34B10
Keywords: nonhomogeneous, fourth-order, four-point, Sturm-Liouville, boundary-value problem, positive solution, uniqueness, dependence on parameter 
@article{EJDE_2010__2010__a262,
     author = {Sun, Jian-Ping and Wang, Xiao-Yun},
     title = {Uniqueness and parameter dependence of solutions of fourth-order four-point nonhomogeneous {BVPs}},
     journal = {Electronic Journal of Differential Equations},
     publisher = {mathdoc},
     volume = {2010},
     year = {2010},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/EJDE_2010__2010__a262/}
}
TY  - JOUR
AU  - Sun, Jian-Ping
AU  - Wang, Xiao-Yun
TI  - Uniqueness and parameter dependence of solutions of fourth-order four-point nonhomogeneous BVPs
JO  - Electronic Journal of Differential Equations
PY  - 2010
VL  - 2010
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/item/EJDE_2010__2010__a262/
LA  - en
ID  - EJDE_2010__2010__a262
ER  - 
%0 Journal Article
%A Sun, Jian-Ping
%A Wang, Xiao-Yun
%T Uniqueness and parameter dependence of solutions of fourth-order four-point nonhomogeneous BVPs
%J Electronic Journal of Differential Equations
%D 2010
%V 2010
%I mathdoc
%U http://geodesic.mathdoc.fr/item/EJDE_2010__2010__a262/
%G en
%F EJDE_2010__2010__a262
Sun, Jian-Ping; Wang, Xiao-Yun. Uniqueness and parameter dependence of solutions of fourth-order four-point nonhomogeneous BVPs. Electronic Journal of Differential Equations, Tome 2010 (2010). http://geodesic.mathdoc.fr/item/EJDE_2010__2010__a262/