Geodesic
Elliptic equations with one-sided critical growth
Electronic journal of differential equations, Tome 2002 (2002)
We consider elliptic equations in bounded domains $\Omega\subset \mathbb{R}^N $ with nonlinearities which have critical growth at $+\infty$ and linear growth $\lambda$ at $-\infty$, with $\lambda greater than \lambda_1$, the first eigenvalue of the Laplacian. We prove that such equations have at least two solutions for certain forcing terms provided $N \ge 6$. In dimensions $N = 3,4,5$ an additional lower order growth term has to be added to the nonlinearity, similarly as in the famous result of Brezis-Nirenberg for equations with critical growth.
Classification : 35J20
Keywords: nonlinear elliptic equation, critical growth, linking structure 
@article{EJDE_2002__2002__a10,
     author = {Calanchi,  Marta and Ruf,  Bernhard},
     title = {Elliptic equations with one-sided critical growth},
     journal = {Electronic journal of differential equations},
     year = {2002},
     volume = {2002},
     zbl = {1022.35009},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/EJDE_2002__2002__a10/}
}
TY  - JOUR
AU  - Calanchi,  Marta
AU  - Ruf,  Bernhard
TI  - Elliptic equations with one-sided critical growth
JO  - Electronic journal of differential equations
PY  - 2002
VL  - 2002
UR  - http://geodesic.mathdoc.fr/item/EJDE_2002__2002__a10/
LA  - en
ID  - EJDE_2002__2002__a10
ER  - 
%0 Journal Article
%A Calanchi,  Marta
%A Ruf,  Bernhard
%T Elliptic equations with one-sided critical growth
%J Electronic journal of differential equations
%D 2002
%V 2002
%U http://geodesic.mathdoc.fr/item/EJDE_2002__2002__a10/
%G en
%F EJDE_2002__2002__a10
Calanchi,  Marta; Ruf,  Bernhard. Elliptic equations with one-sided critical growth. Electronic journal of differential equations, Tome 2002 (2002). http://geodesic.mathdoc.fr/item/EJDE_2002__2002__a10/