A variational approach to the equation \({\triangle}u+Ku^{{n+2}/{n- 2}}=0\) in \(\mathbb{R}^ n\)

DOI10.1007/BF00378166zbMath0803.35033MaRDI QIDQ1261959

Henrik Egnell, Gabriele Bianchi

Publication date: 7 September 1993

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

zbMATH Keywords

radial solutionscritical Sobolev exponentmountain pass setting

Mathematics Subject Classification ID

Nonlinear elliptic equations (35J60) Variational methods for second-order elliptic equations (35J20)

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Cites Work

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• The scalar-curvature problem on the standard three-dimensional sphere
• The concentration-compactness principle in the calculus of variations. The limit case. II
• On the elliptic equation \(\Delta u+Ku^{(n+2)/(n-2)}=0\) and related topics
• Conformal metrics with prescribed scalar curvature
• A note on the Sobolev inequality
• Asymptotic results for finite energy solutions of semilinear elliptic equations
• An ODE approach to the equation \(\Delta u + Ku^{{n+2}\over{n-2}}=0\) in \(\mathbb{R}^ n\)
• Existence and conformal deformation of metrics with prescribed Gaussian and scalar curvatures
• Addendum to ``A perturbation result in prescribing scalar curvature on \(S^ n\)
• Positive Solutions of Semilinear Equations in Cones
• Positive radial solutions for and related topics