Revista Matemática Iberoamericana

Critical nonlinear elliptic equations with singularities and cylindrical symmetry

Marino Badiale and Enrico Serra

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Motivated by a problem arising in astrophysics we study a nonlinear elliptic equation in $\mathbb{R}^{N}$ with cylindrical symmetry and with singularities on a whole subspace of $\mathbb{R}^{N}$. We study the problem in a variational framework and, as the nonlinearity also displays a critical behavior, we use some suitable version of the Concentration-Compactness Principle. We obtain several results on existence and nonexistence of solutions.

Article information

Rev. Mat. Iberoamericana, Volume 20, Number 1 (2004), 33-66.

First available in Project Euclid: 2 April 2004

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Primary: 35J20: Variational methods for second-order elliptic equations 35B33: Critical exponents

critical exponents loss of compactness cylindrical symmetry singularities


Badiale, Marino; Serra, Enrico. Critical nonlinear elliptic equations with singularities and cylindrical symmetry. Rev. Mat. Iberoamericana 20 (2004), no. 1, 33--66.

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