Yamabe type equations with sign-changing nonlinearities on non-compact Riemannian manifolds

DOI10.1016/j.jfa.2014.10.016zbMath1396.58016OpenAlexW1969155423MaRDI QIDQ473174

Bruno Bianchini, Luciano Mari, Marco Rigoli

Publication date: 21 November 2014

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

Full work available at URL: https://doi.org/10.1016/j.jfa.2014.10.016

zbMATH Keywords

comparisonSchrödinger operatorYamabe equationsign-changing nonlinearity

Mathematics Subject Classification ID

Asymptotic behavior of solutions to PDEs (35B40) Elliptic equations on manifolds, general theory (58J05) Growth and boundedness of solutions to ordinary differential equations (34C11) Existence problems for PDEs: global existence, local existence, non-existence (35A01) Methods of global Riemannian geometry, including PDE methods; curvature restrictions (53C21) Positive solutions to PDEs (35B09) Semilinear elliptic equations with Laplacian, bi-Laplacian or poly-Laplacian (35J91) PDEs on manifolds (35R01)

Related Items

Yamabe type equations with a sign-changing nonlinearity, and the prescribed curvature problem, Improved higher order Poincaré inequalities on the hyperbolic space via Hardy-type remainder terms, Density and spectrum of minimal submanifolds in space forms, On the $1/H$-flow by $p$-Laplace approximation: new estimates via fake distances under Ricci lower bounds, Recent rigidity results for graphs with prescribed mean curvature, Remarks on mean curvature flow solitons in warped products, An optimal improvement for the Hardy inequality on the hyperbolic space and related manifolds, A note on Killing fields and CMC hypersurfaces, Nonexistence results for elliptic differential inequalities with a potential on Riemannian manifolds, On some aspects of oscillation theory and geometry

Cites Work

• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Function theory on manifolds which possess a pole
• On bounded entire solutions of semilinear elliptic equations
• A note on bounded positive entire solutions of semilinear elliptic equations
• On the inequality \(\Delta u \geqq f (u)\)
• Entire solutions of singular elliptic inequalities on complete manifolds
• Keller-Osserman conditions for diffusion-type operators on Riemannian manifolds
• On the elliptic equation \(\Delta u+Ku^{(n+2)/(n-2)}=0\) and related topics
• On conformal scalar curvature equations in \({\mathbb{R}}^ n\)
• Positive solutions of elliptic equations
• Scalar curvature and conformal deformation of hyperbolic space
• A Liouville theorem for a class of superlinear elliptic equations on cones
• Positive solutions to \(\Delta u-Vu+Wu^ p=0\) and its parabolic counterpart in noncompact manifolds.
• Positive solutions of Yamabe-type equations on the Heisenberg group
• Vanishing and finiteness results in geometric analysis. A generalization of the Bochner technique
• On the equivalence of stochastic completeness and Liouville and Khas’minskii conditions in linear and nonlinear settings
• On solutions of δu=f(u)
• Positive solutions of nonlinear elliptic equations involving critical sobolev exponents
• Weighted Poincaré inequality and rigidity of complete manifolds
• Existence and non-existence results for a logistic-type equation on manifolds
• On the Elliptic Equation D i [ a ij (x)D j U - k(x)U + K(x)U p = 0]
• On the Elliptic Equations Δu = K(x)u σ and Δu = K(x)e 2u
• The structure of complete stable minimal surfaces in 3-manifolds of non-negative scalar curvature
• Analytic and geometric background of recurrence and non-explosion of the Brownian motion on Riemannian manifolds
• Nonexistence and uniqueness of positive solutions of Yamabe type equations on nonpositively curved manifolds
• Maximum principles on Riemannian manifolds and applications
• On some aspects of oscillation theory and geometry
• An Exterior Dirichlet Problem with Applications to Some Nonlinear Equations Arising in Geometry