An elementary proof of the uniqueness of positive radial solutions of a quasilinear Dirichlet problem

DOI10.1007/BF00381159zbMath0806.35031OpenAlexW1971142210MaRDI QIDQ1337987

Publication date: 14 November 1994

Published in: Archive for Rational Mechanics and Analysis (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/bf00381159

zbMATH Keywords

quasilinear elliptic equation generalized Pohožaev-type variational identity uniqueness of positive radial solutions

Mathematics Subject Classification ID

Nonlinear boundary value problems for linear elliptic equations (35J65) Invariance and symmetry properties for PDEs on manifolds (58J70)

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Cites Work