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

### Summary

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

35J20, 35K20

### Keywords/Phrases

elliptic equations, unbounded domains, critical exponents, variational methods