Alves, C. O.; Goncalves, J. V.; Miyagaki, O. H. On elliptic equations in \(\mathbb R^ N\) with critical exponents. (English) Zbl 0854.35037 Electron. J. Differ. Equ. 1996, No. 9, 11 p. (1996). 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 \(2^*= 2N/(N- 2)\). Cited in 2 Documents MSC: 35J65 Nonlinear boundary value problems for linear elliptic equations 35J20 Variational methods for second-order elliptic equations Keywords:removable singularity; Ekeland’s principle; Mountain Pass Theorem PDFBibTeX XML Full Text: EuDML EMIS