A prescribed scalar curvature-type equation: Almost critical manifolds and multiple solutions.

DOI10.1016/j.jfa.2003.07.004zbMath1173.35425OpenAlexW2167957515MaRDI QIDQ1421848

Pierpaolo Esposito, Gianni Mancini

Publication date: 3 February 2004

Published in: Journal of Functional Analysis (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/j.jfa.2003.07.004

zbMATH Keywords

scalar curvatureasymptotic analysiscritical growthfinite-dimensional reductionnonlinear ellptic boundary value problem

Mathematics Subject Classification ID

Boundary value problems for second-order elliptic equations (35J25) Critical exponents in context of PDEs (35B33) Methods of global Riemannian geometry, including PDE methods; curvature restrictions (53C21)

Related Items (2)

Compactness and existence results of the prescribing fractional \(Q\)-curvature problem on \(\mathbb{S}^n\) ⋮ Concentrating solutions for a planar elliptic problem involving nonlinearities with large exponent

Cites Work

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• A global compactness result for elliptic boundary value problems involving limiting nonlinearities
• Asymptotic approach to singular solutions for nonlinear elliptic equations involving critical Sobolev exponent
• Proof of two conjectures of H. Brezis and L. A. Peletier
• Bifurcation from infinity in a nonlinear elliptic equation involving the limiting Sobolev exponent
• On the elliptic equation \(\Delta u+Ku^{(n+2)/(n-2)}=0\) and related topics
• Symmetry breaking in Hamiltonian systems
• Symmetry and related properties via the maximum principle
• A perturbation result in prescribing scalar curvature on \(S^ n\)
• Concentration of solutions to elliptic equations with critical nonlinearity
• Some continuation and variational methods for positive solutions of nonlinear elliptic eigenvalue problems
• Perturbation of \(\Delta u+u^{(N+2)/(N-2)}=0\), the scalar curvature problem in \(\mathbb{R}^N\), and related topics
• The scalar curvature equation on 2- and 3-spheres
• Homoclinics: Poincaré-Melnikov type results via a variational approach
• Multiple solutions of nonhomogeneous elliptic equation with critical nonlinearity
• Homoclinics and chaotic behaviour for perturbed second order systems
• A sharp solvability condition in higher dimensions for some Brezis-Nirenberg type equation
• The role of the Green's function in a nonlinear elliptic equation involving the critical Sobolev exponent
• Some existence results for the scalar curvature problem via Morse theory
• Asymptotic behaviour of a nonlinear elliptic equation with critical Sobolev exponent: the radial case. II
• A note on the scalar curvature problem in the presence of symmetries
• Prescribing scalar curvature on \(\mathbb{S}^ n\) and related problems. I
• Asymptotics for some quasilinear elliptic equations
• Concentration of solutions for a nonlinear elliptic problem with nearly critical exponent
• Perturbations of Paneitz-Branson operators on \(S^n\)
• Positive solutions of nonlinear elliptic equations involving critical sobolev exponents
• On a nonlinear elliptic equation involving the critical sobolev exponent: The effect of the topology of the domain
• Geometry and topology of the boundary in the critical Neumann problem.
• The role of the mean curvature in semilinear neumann problem involving critical exponent
• Non-compactness and multiplicity results for the Yamabe problem on \(S^n\)
• On the symmetric scalar curvature problem on \(S^n\)
• Asymptotic behavior of positive solutions of quasilinear elliptic equations with critical Sobolev growth
• Asymptotic behaviour of a nonlinear elliptic equation with critical Sobolev exponent: the radial case.

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