Geodesic
Existence and uniqueness of solutions for fourth-order boundary-value problems in Banach spaces
Electronic journal of differential equations, Tome 2009 (2009)
This article concerns the fourth-order boundary-value problem

$\displaylines{ x^{(4)}(t)=f(t,x(t),x''(t)),\quad t\in (0,1),\cr x(0)=x(1)=x''(0)=x''(1)=\theta, }$

in a Banach space. We present some spectral conditions, on the nonlinearity $f(t,u,v)$, to guarantee the existence and uniqueness of solutions. Our method is different from the one used in the references, even the above problem in a scalar space.
Classification : 47H10
Keywords: spectral conditions, Mönch fixed-point theorem 
@article{EJDE_2009__2009__a192,
     author = {Cui,  Yujun and Zou,  Yumei},
     title = {Existence and uniqueness of solutions for fourth-order boundary-value problems in {Banach} spaces},
     journal = {Electronic journal of differential equations},
     year = {2009},
     volume = {2009},
     zbl = {1191.34079},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/EJDE_2009__2009__a192/}
}
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VL  - 2009
UR  - http://geodesic.mathdoc.fr/item/EJDE_2009__2009__a192/
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%A Zou,  Yumei
%T Existence and uniqueness of solutions for fourth-order boundary-value problems in Banach spaces
%J Electronic journal of differential equations
%D 2009
%V 2009
%U http://geodesic.mathdoc.fr/item/EJDE_2009__2009__a192/
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%F EJDE_2009__2009__a192
Cui,  Yujun; Zou,  Yumei. Existence and uniqueness of solutions for fourth-order boundary-value problems in Banach spaces. Electronic journal of differential equations, Tome 2009 (2009). http://geodesic.mathdoc.fr/item/EJDE_2009__2009__a192/