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Badiale, Marino; Serra, Enrico

Critical nonlinear elliptic equations with singularities and cylindrical symmetry. (English) Zbl 1330.35137

Rev. Mat. Iberoam. 20, No. 1, 33-66 (2004).
Summary: Motivated by a problem arising in astrophysics we study a nonlinear elliptic equation in RN 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.

Cited in 7 Documents

MSC:

35J60 Nonlinear elliptic equations
35B33 Critical exponents in context of PDEs
35J20 Variational methods for second-order elliptic equations

Keywords:

critical exponents; loss of compactness; cylindrical symmetry; singularities
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\textit{M. Badiale} and \textit{E. Serra}, Rev. Mat. Iberoam. 20, No. 1, 33--66 (2004; Zbl 1330.35137)
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References:

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