Existence and nonexistence results for quasilinear elliptic equations involving the \(p\)-Laplacian with a critical potential

DOI10.1007/s10231-002-0064-yzbMath1223.35151OpenAlexW2010918519MaRDI QIDQ2504767

Ireneo Peral Alonso, Boumediene Abdellaoui

Publication date: 28 September 2006

Published in: Annali di Matematica Pura ed Applicata. Serie Quarta (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/s10231-002-0064-y

Mathematics Subject Classification ID

Partial differential inequalities and systems of partial differential inequalities (35R45) Nonlinear elliptic equations (35J60) Existence problems for PDEs: global existence, local existence, non-existence (35A01)

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Cites Work