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__a162,
     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__a162/}
}
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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__a162/