## On elliptic equations in $$\mathbb R^ N$$ with critical exponents.(English)Zbl 0854.35037

Summary: We use variational arguments – namely Ekeland’s principle and the Mountain Pass Theorem – to study the equation $- \Delta u+ a(x) u= \lambda u^q+ u^{2^*- 1}\quad \text{in } \mathbb{R}^N.$ The main concern is overcoming compactness difficulties due both to the unboundedness of the domain $$\mathbb{R}^N$$, and the presence of the critical exponent $$2^*= 2N/(N- 2)$$.

### MSC:

 35J65 Nonlinear boundary value problems for linear elliptic equations 35J20 Variational methods for second-order elliptic equations
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