The scalar curvature equation on \(\mathbb R^N\)

DOI10.1016/S0362-546X(99)00428-9zbMath1116.35050OpenAlexW164911720MaRDI QIDQ5946009

Ezzat S. Noussair, Shusen Yan

Publication date: 14 October 2001

Published in: Nonlinear Analysis. Theory, Methods \& Applications. Series A: Theory and Methods (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/s0362-546x(99)00428-9

zbMATH Keywords

multiplicity of solutionsalmost critical exponentnonlinear elliptic problemsscalar curvature equation

Mathematics Subject Classification ID

Critical exponents in context of PDEs (35B33) Nonlinear elliptic equations (35J60)

Related Items (12)

Constructing solutions for the prescribed scalar curvature problem via local Pohozaev identities ⋮ On the prescribed scalar curvature problem with very degenerate prescribed functions ⋮ Infinitely many solutions for the prescribed curvature problem of polyharmonic operator ⋮ Doubling the equatorial for the prescribed scalar curvature problem on \(\mathbb{S}^N\) ⋮ Existence of multi-bump solutions for a system with critical exponent in \(\mathbb{R}^N\) ⋮ Infinitely many solutions for the prescribed scalar curvature problem on \(\mathbb S^N\) ⋮ Infinitely many non-radial solutions for the prescribed curvature problem of fractional operator ⋮ Multiplicity of ground states for the scalar curvature equation ⋮ Solutions for fractional Schrödinger equation involving critical exponent via local Pohozaev identities ⋮ The concentrated solutions on the nonhomogeneous scalar curvature problem ⋮ Concentration of solutions for the scalar curvature equation on \(\mathbb{R}^n\) ⋮ Multiplicity of radial ground states for the scalar curvature equation without reciprocal symmetry

Cites Work

• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• The scalar-curvature problem on the standard three-dimensional sphere
• A note on bounded positive entire solutions of semilinear elliptic equations
• A global compactness result for elliptic boundary value problems involving limiting nonlinearities
• The concentration-compactness principle in the calculus of variations. The limit case. I
• On the elliptic equation \(\Delta u+Ku^{(n+2)/(n-2)}=0\) and related topics
• Conformal metrics with prescribed scalar curvature
• On conformal scalar curvature equations in \({\mathbb{R}}^ n\)
• Existence of positive entire solutions of some semilinear elliptic equations
• Positive entire solutions of the equation \(\Delta{}u+f(x,u)=0\)
• An ODE approach to the equation \(\Delta u + Ku^{{n+2}\over{n-2}}=0\) in \(\mathbb{R}^ n\)
• Equations différentielles non linéaires et problème de Yamabe concernant la courbure scalaire
• A variational approach to the equation \({\triangle}u+Ku^{{n+2}/{n- 2}}=0\) in \(\mathbb{R}^ n\)
• The effect of the graph topology on a semilinear elliptic equation with critical exponent
• Prescribing scalar curvature on \(\mathbb{S}^ 3\), \(\mathbb{S}^ 4\) and related problems
• Existence of positive radial solutions to \(\Delta u+K(| x| )u^ p=0\) in \(\mathbb R^ n\)
• Multiple positive solutions of a scalar field equation in \(\mathbb{R}^n\)
• The role of the Green's function in a nonlinear elliptic equation involving the critical Sobolev exponent
• Prescribing scalar curvature on \(\mathbb{S}^ n\) and related problems. I
• Multiple finite energy solutions of critical semilinear field equations
• The scalar curvature equation on \(\mathbb{R}^ n\) and \(S^ n\)
• Positive solutions of nonlinear elliptic equations involving critical sobolev exponents
• Decaying Solutions of Semilinear Elliptic Equations in ${\bf R}^N $
• On a nonlinear elliptic equation involving the critical sobolev exponent: The effect of the topology of the domain
• Positive Solutions of Δu + K(x)u p = 0 Without Decay Conditions on K(x)
• Positive Finite Energy Solutions of Critical Semilinear Elliptic Problems
• Positive radial solutions for and related topics
• High-energy solutions for a nonlinear elliptic problem with slightly supercritical exponent
• On –δu = K(x)u⁵ in ℝ³
• Non-existence and symmetry of solutions to the scalar curvature equation
• Prescribing scalar curvature on Sn and related problems, part II: Existence and compactness

This page was built for publication: The scalar curvature equation on \(\mathbb R^N\)