On elliptic equations in R^{<small>N</small>} with critical exponents

Abstract

Principle and the Mountain Pass Theorem-- to study the equation $$-Delta u + a(x)u = lambda u^q + u^{2^*-1} quad{ m in } R^N,.$$ The main concern is overcoming compactness difficulties due both to the unboundedness of the domain $R^N$, and the presence of the critical exponent $2^*= 2N/(N-2)$.

Keywords

• Elliptic equations
• unbounded domains
• critical exponents
• variational methods.