Geodesic
Nonlinear singular Navier problem of fourth order
Electronic journal of differential equations, Tome 2003 (2003)
We present an existence result for a nonlinear singular differential equation of fourth order with Navier boundary conditions. Under appropriate conditions on the nonlinearity

$\displaylines{ L^{2}u=L(Lu) =f(.,u,Lu)\quad \hbox{a.e. in }(0,1), \cr u'(0) =0,\quad (Lu) '(0)=0,\quad u(1) =0,\quad Lu(1) =0. }$

has a positive solution behaving like $(1-t)$ on $[0,1]$. Here $L$ is a differential operator of second order, $Lu=\frac{1}{A}(Au')'$. For $f(t,x,y)=f(t,x)$, we prove a uniqueness result. Our approach is based on estimates for Green functions and on Schauder's fixed point theorem.
Classification : 34B15, 34B27
Keywords: nonlinear singular Navier problem, Green function, positive solution 
@article{EJDE_2003__2003__a71,
     author = {Masmoudi,  Syrine and Zribi,  Malek},
     title = {Nonlinear singular {Navier} problem of fourth order},
     journal = {Electronic journal of differential equations},
     year = {2003},
     volume = {2003},
     zbl = {1022.34012},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/EJDE_2003__2003__a71/}
}
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AU  - Zribi,  Malek
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%A Zribi,  Malek
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%J Electronic journal of differential equations
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Masmoudi,  Syrine; Zribi,  Malek. Nonlinear singular Navier problem of fourth order. Electronic journal of differential equations, Tome 2003 (2003). http://geodesic.mathdoc.fr/item/EJDE_2003__2003__a71/