Alves, C.O.; Goncalves, J.V.; Miyagaki, O.H.

On elliptic equations in $\Bbb R\sp N$ with critical exponents

Electron. J. Differ. Equ. 1996(9), (1996)


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 $2^*= 2N/(N-2)$.

Mathematics Subject Classification

35J20, 35K20


elliptic equations, unbounded domains, critical exponents, variational methods