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.
Critical nonlinear elliptic equations with singularities and cylindrical symmetry / M. Badiale, E. Serra. - In: REVISTA MATEMATICA IBEROAMERICANA. - ISSN 0213-2230. - 20(2004):1(2004), pp. 33-66.
Critical nonlinear elliptic equations with singularities and cylindrical symmetry
E. SerraUltimo
2004
Abstract
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.
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