Geodesic
Elliptic equations with one-sided critical growth
Electronic Journal of Differential Equations, Tome 2002 (2002).

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

Summary: 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 
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     author = {Calanchi, Marta and Ruf, Bernhard},
     title = {Elliptic equations with one-sided critical growth},
     journal = {Electronic Journal of Differential Equations},
     publisher = {mathdoc},
     volume = {2002},
     year = {2002},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/EJDE_2002__2002__a10/}
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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/