Geodesic
Existence and multiplicity of solutions for divergence type elliptic equations
Electronic journal of differential equations, Tome 2011 (2011)
We establish the existence and multiplicity of weak solutions of a problem involving a uniformly convex elliptic operator in divergence form. We find one nontrivial solution by the mountain pass lemma, when the nonlinearity has a $(p-1)$-superlinear growth at infinity, and two nontrivial solutions by minimization and mountain pass when the nonlinear term has a $(p-1)$-sublinear growth at infinity.
Classification : 35A15, 35J20, 35J62
Keywords: nonlinear elliptic equations, uniformly convex, mountain pass lemma, three critical points theorem 
@article{EJDE_2011__2011__a54,
     author = {Zhao,  Lin and Zhao,  Peihao and Xie,  Xiaoxia},
     title = {Existence and multiplicity of solutions for divergence type elliptic equations},
     journal = {Electronic journal of differential equations},
     year = {2011},
     volume = {2011},
     zbl = {1213.35227},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/EJDE_2011__2011__a54/}
}
TY  - JOUR
AU  - Zhao,  Lin
AU  - Zhao,  Peihao
AU  - Xie,  Xiaoxia
TI  - Existence and multiplicity of solutions for divergence type elliptic equations
JO  - Electronic journal of differential equations
PY  - 2011
VL  - 2011
UR  - http://geodesic.mathdoc.fr/item/EJDE_2011__2011__a54/
LA  - en
ID  - EJDE_2011__2011__a54
ER  - 
%0 Journal Article
%A Zhao,  Lin
%A Zhao,  Peihao
%A Xie,  Xiaoxia
%T Existence and multiplicity of solutions for divergence type elliptic equations
%J Electronic journal of differential equations
%D 2011
%V 2011
%U http://geodesic.mathdoc.fr/item/EJDE_2011__2011__a54/
%G en
%F EJDE_2011__2011__a54
Zhao,  Lin; Zhao,  Peihao; Xie,  Xiaoxia. Existence and multiplicity of solutions for divergence type elliptic equations. Electronic journal of differential equations, Tome 2011 (2011). http://geodesic.mathdoc.fr/item/EJDE_2011__2011__a54/