Geodesic
On elliptic equations in \(\mathbb R^ N\) with critical exponents
Electronic journal of differential equations, Tome 1996 (1996) no. 9
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 \(\mathbb {R^} {N\)} with critical exponents},
     journal = {Electronic journal of differential equations},
     year = {1996},
     volume = {1996},
     number = {9},
     zbl = {0854.35037},
     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 \(\mathbb R^ N\) with critical exponents. Electronic journal of differential equations, Tome 1996 (1996) no. 9. http://geodesic.mathdoc.fr/item/EJDE_1996__1996_9_a0/