Geodesic
On elliptic equations in $\Bbb R\sp N$ with critical exponents
Electronic Journal of Differential Equations, Tome 1996 (1996) no. 9.

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

Summary: In this note we use variational arguments -namely Ekeland's Principle and the Mountain Pass Theorem- to study the equation $$-\Delta u + a(x)u = \lambda u^q + u^{2^*-1}\quad {\rm in\ } R^N\,.$$ The main concern is overcoming compactness difficulties due both to the unboundedness of the domain $R^N$, and the presence of the critical exponent $2^*= 2N/(N-2)$.
Classification : 35J20, 35K20
Keywords: elliptic equations, unbounded domains, critical exponents, variational methods 
@article{EJDE_1996__1996_9_a0,
     author = {Alves, C.O. and Goncalves, J.V. and Miyagaki, O.H.},
     title = {On elliptic equations in $\Bbb R\sp N$ with critical exponents},
     journal = {Electronic Journal of Differential Equations},
     publisher = {mathdoc},
     volume = {1996},
     number = {9},
     year = {1996},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/EJDE_1996__1996_9_a0/}
}
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Alves, C.O.; Goncalves, J.V.; Miyagaki, O.H. On elliptic equations in $\Bbb R\sp N$ with critical exponents. Electronic Journal of Differential Equations, Tome 1996 (1996) no. 9. http://geodesic.mathdoc.fr/item/EJDE_1996__1996_9_a0/