Geodesic
Nonlinear singular Navier problem of fourth order
Electronic Journal of Differential Equations, Tome 2003 (2003).

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

Summary: 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__a171,
     author = {Masmoudi, Syrine and Zribi, Malek},
     title = {Nonlinear singular {Navier} problem of fourth order},
     journal = {Electronic Journal of Differential Equations},
     publisher = {mathdoc},
     volume = {2003},
     year = {2003},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/EJDE_2003__2003__a171/}
}
TY  - JOUR
AU  - Masmoudi, Syrine
AU  - Zribi, Malek
TI  - Nonlinear singular Navier problem of fourth order
JO  - Electronic Journal of Differential Equations
PY  - 2003
VL  - 2003
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/item/EJDE_2003__2003__a171/
LA  - en
ID  - EJDE_2003__2003__a171
ER  - 
%0 Journal Article
%A Masmoudi, Syrine
%A Zribi, Malek
%T Nonlinear singular Navier problem of fourth order
%J Electronic Journal of Differential Equations
%D 2003
%V 2003
%I mathdoc
%U http://geodesic.mathdoc.fr/item/EJDE_2003__2003__a171/
%G en
%F EJDE_2003__2003__a171
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__a171/