Geodesic
Existence and uniqueness of solutions for fourth-order boundary-value problems in Banach spaces
Electronic Journal of Differential Equations, Tome 2009 (2009).

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

Summary: 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__a92,
     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},
     publisher = {mathdoc},
     volume = {2009},
     year = {2009},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/EJDE_2009__2009__a92/}
}
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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__a92/