Liouville-type theorems for semilinear elliptic equations involving the Sobolev exponent

DOI10.1007/PL00004641zbMath0915.35036OpenAlexW2011944000MaRDI QIDQ1273147

Chang-Shou Lin

Publication date: 13 July 1999

Published in: Mathematische Zeitschrift (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/pl00004641

zbMATH Keywords

nonexistencecritical Sobolev exponent

Mathematics Subject Classification ID

Nonlinear elliptic equations (35J60) Oscillation, zeros of solutions, mean value theorems, etc. in context of PDEs (35B05)

Related Items (11)

PRESCRIBING A FOURTH ORDER CONFORMAL INVARIANT ON THE STANDARD SPHERE — PART I: A PERTURBATION RESULT ⋮ Non-existence for a semi-linear fractional system with Sobolev exponents via direct method of moving spheres ⋮ Unnamed Item ⋮ Liouville-type theorems for semilinear elliptic systems ⋮ Nonexistence of ground states of \(-\Delta u = u^p - u^q\) ⋮ Estimates of the scalar curvature equation via the method of moving planes III ⋮ Nonexistence of positive solutions of \(-\Delta u = K(x)u^p\) in \(\mathbb R^n\) ⋮ Local estimate on singular solution to scalar curvature equation ⋮ Liouville-type theorems for conformal Gaussian curvature equations in \(\mathbb R^2\). ⋮ The sharp exponent in the study of the nonlocal Hénon equation in \(\mathbb{R}^N\): a Liouville theorem and an existence result ⋮ Existence and Liouville-type theorems for some indefinite quasilinear elliptic problems with potentials vanishing at infinity

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