Geodesic
Existence of solutions for some third-order boundary-value problems
Electronic journal of differential equations, Tome 2008 (2008)
In this paper concerns the third-order boundary-value problem

$\displaylines{ u'''(t)+ f(t, u(t),u'(t), u''(t))=0, \quad 0 t 1, \cr r_1 u(0) - r_2 u' (0)= r_3 u(1) + r_4 u'(1)= u''(0)=0. }$

By placing certain restrictions on the nonlinear term f, we prove the existence of at least one solution to the boundary-value problem with the use of lower and upper solution method and of Schauder fixed-point theorem. The construction of lower or upper solutions is also presented.
Classification : 34B15
Keywords: third-order boundary-value problem, lower and upper solutions, fixed-point theorem 
@article{EJDE_2008__2008__a78,
     author = {Bai,  Zhanbing},
     title = {Existence of solutions for some third-order boundary-value problems},
     journal = {Electronic journal of differential equations},
     year = {2008},
     volume = {2008},
     zbl = {1141.34307},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/EJDE_2008__2008__a78/}
}
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Bai,  Zhanbing. Existence of solutions for some third-order boundary-value problems. Electronic journal of differential equations, Tome 2008 (2008). http://geodesic.mathdoc.fr/item/EJDE_2008__2008__a78/