Motivated by a problem arising in astrophysics, we study a nonlinear elliptic equation in R^N with cylindrical symmetry and with singularities on a whole subspace of 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.
BADIALE, Marino;
2004-01-01
Abstract
Motivated by a problem arising in astrophysics, we study a nonlinear elliptic equation in R^N with cylindrical symmetry and with singularities on a whole subspace of 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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