Stationary Kirchhoff systems in closed 3-dimensional manifolds

DOI10.1007/s00526-015-0858-6zbMath1348.35075OpenAlexW2461335387MaRDI QIDQ745584

Emmanuel Hebey, Pierre-Damien Thizy

Publication date: 14 October 2015

Published in: Calculus of Variations and Partial Differential Equations (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/s00526-015-0858-6

zbMATH Keywords

Yamabe equationSobolev critical levelstationary Kirchhoff system

Mathematics Subject Classification ID

Critical exponents in context of PDEs (35B33) A priori estimates in context of PDEs (35B45) Elliptic equations on manifolds, general theory (58J05) Second-order elliptic systems (35J47) PDEs on manifolds (35R01)

Related Items (9)

A priori bounds and existence of positive solutions of an elliptic system of Kirchhoff type in three or four space dimensions ⋮ Multiplicity of solutions for critical Kirchhoff type equations ⋮ Stationary Kirchhoff equations with powers ⋮ Stationary Kirchhoff equations involving critical growth and vanishing potential ⋮ Multiplicity of positive solutions for Kirchhoff systems ⋮ Stationary Kirchhoff systems in closed high dimensional manifolds ⋮ Least energy solutions to an elliptic system with couplings on Kirchhoff term and nonlinear part ⋮ Recent results on stationary critical Kirchhoff systems in closed manifolds ⋮ Infinitely many periodic solutions for a class of fractional Kirchhoff problems

Cites Work

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• Existence of a positive solution to Kirchhoff-type problems without compactness conditions
• A global compactness result for elliptic boundary value problems involving limiting nonlinearities
• Nontrivial solutions of Kirchhoff-type problems via the Yang index
• Stability for strongly coupled critical elliptic systems in a fully inhomogeneous medium
• Bounded stability for strongly coupled critical elliptic systems below the geometric threshold of the conformal Laplacian
• Global solvability for the degenerate Kirchhoff equation with real analytic data
• On the proof of the positive mass conjecture in general relativity
• A new proof of the positive energy theorem.
• Schrödinger-Poisson systems in the 3-sphere
• Resonant states for the static Klein-Gordon-Maxwell-Proca system
• The Lin-Ni's conjecture for vector-valued Schrödinger equations in the closed case
• Non-existence results for semilinear cooperative elliptic systems via moving spheres
• Compactness and stability for nonlinear elliptic equations
• Dual variational methods in critical point theory and applications
• Stationary Kirchhoff systems in closed high dimensional manifolds
• High energy solutions of systems of Kirchhoff-type equations in R N
• Asymptotic symmetry and local behavior of semilinear elliptic equations with critical sobolev growth
• A priori bounds for positive solutions of nonlinear elliptic equations
• YAMABE TYPE EQUATIONS ON THREE DIMENSIONAL RIEMANNIAN MANIFOLDS
• On the Well-Posedness of the Kirchhoff String

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