Geodesic
Existence of bounded solutions for nonlinear fourth-order elliptic equations with strengthened coercivity and lower-order terms with natural growth
Electronic journal of differential equations, Tome 2013 (2013)
In this article, we consider nonlinear elliptic fourth-order equations with the principal part satisfying a strengthened coercivity condition, and a lower-order term having a "natural" growth with respect to the derivatives of the unknown function. We assume that there is an absorption term in the equation, but we do not assume that the lower-order term satisfies the sign condition with respect to unknown function. We prove the existence of bounded generalized solutions for the Dirichlet problem, and present some a priori estimates.
Classification : 35B45, 35B65, 35J40, 35J62
Keywords: nonlinear elliptic equations, strengthened coercivity, lower-order term, natural growth, Dirichlet problem, bounded solution, L-infinity-estimate 
@article{EJDE_2013__2013__a120,
     author = {Voitovich,  Michail V.},
     title = {Existence of bounded solutions for nonlinear fourth-order elliptic equations with strengthened coercivity and lower-order terms with natural growth},
     journal = {Electronic journal of differential equations},
     year = {2013},
     volume = {2013},
     zbl = {1290.35073},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/EJDE_2013__2013__a120/}
}
TY  - JOUR
AU  - Voitovich,  Michail V.
TI  - Existence of bounded solutions for nonlinear fourth-order elliptic equations with strengthened coercivity and lower-order terms with natural growth
JO  - Electronic journal of differential equations
PY  - 2013
VL  - 2013
UR  - http://geodesic.mathdoc.fr/item/EJDE_2013__2013__a120/
LA  - en
ID  - EJDE_2013__2013__a120
ER  - 
%0 Journal Article
%A Voitovich,  Michail V.
%T Existence of bounded solutions for nonlinear fourth-order elliptic equations with strengthened coercivity and lower-order terms with natural growth
%J Electronic journal of differential equations
%D 2013
%V 2013
%U http://geodesic.mathdoc.fr/item/EJDE_2013__2013__a120/
%G en
%F EJDE_2013__2013__a120
Voitovich,  Michail V. Existence of bounded solutions for nonlinear fourth-order elliptic equations with strengthened coercivity and lower-order terms with natural growth. Electronic journal of differential equations, Tome 2013 (2013). http://geodesic.mathdoc.fr/item/EJDE_2013__2013__a120/