Geodesic
Uniqueness and parameter dependence of solutions of fourth-order four-point nonhomogeneous BVPs
Electronic journal of differential equations, Tome 2010 (2010)
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},
     year = {2010},
     volume = {2010},
     zbl = {1201.34026},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/EJDE_2010__2010__a262/}
}
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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
UR  - http://geodesic.mathdoc.fr/item/EJDE_2010__2010__a262/
LA  - en
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%A Wang,  Xiao-Yun
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%J Electronic journal of differential equations
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%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/