Yamabe type equations with a sign-changing nonlinearity, and the prescribed curvature problem
From MaRDI portal
Publication:264470
DOI10.1016/j.jde.2016.01.031zbMath1337.58012arXiv1404.3118OpenAlexW2254233064MaRDI QIDQ264470
Luciano Mari, Bruno Bianchini, Marco Rigoli
Publication date: 31 March 2016
Published in: Journal of Differential Equations (Search for Journal in Brave)
Full work available at URL: https://arxiv.org/abs/1404.3118
Asymptotic behavior of solutions to PDEs (35B40) Elliptic equations on manifolds, general theory (58J05) Growth and boundedness of solutions to ordinary differential equations (34C11) Methods of global Riemannian geometry, including PDE methods; curvature restrictions (53C21) Positive solutions to PDEs (35B09) Quasilinear elliptic equations with (p)-Laplacian (35J92)
Related Items
Improved \(L^p\)-Poincaré inequalities on the hyperbolic space, Hardy-Rellich and second order Poincaré identities on the hyperbolic space via Bessel pairs, Lichnerowicz-type equations on complete manifolds, On the $1/H$-flow by $p$-Laplace approximation: new estimates via fake distances under Ricci lower bounds, An optimal improvement for the Hardy inequality on the hyperbolic space and related manifolds, Sharp Poincaré-Hardy and Poincaré-Rellich inequalities on the hyperbolic space, Hardy and Rellich inequalities for submanifolds in Hadamard spaces, New sharp Hardy and Rellich type inequalities on Cartan–Hadamard manifolds and their improvements
Cites Work
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- The connectivity at infinity of a manifold and \(L^{q, p}\)-Sobolev inequalities
- Yamabe type equations with sign-changing nonlinearities on non-compact Riemannian manifolds
- On the role of gradient terms in coercive quasilinear differential inequalities on Carnot groups
- Liouville type theorems for \(\varphi\)-subharmonic functions.
- Hardy inequalities on Riemannian manifolds and applications
- On bounded entire solutions of semilinear elliptic equations
- A note on bounded positive entire solutions of semilinear elliptic equations
- A ground state alternative for singular Schrödinger operators
- On positive entire solutions of indefinite semilinear elliptic equations
- Ground state alternative for \(p\)-Laplacian with potential term
- Qualitative properties for solutions of singular elliptic inequalities on complete manifolds
- ``A priori estimates, uniqueness and existence of positive solutions of Yamabe type equations on complete manifolds
- The maximum principle
- Optimal \(L^{p}\) Hardy-type inequalities
- Conformal deformations of complete manifolds with negative curvature
- Singular solutions of the \(p\)-Laplace equation
- Structure of positive solutions to \((-\Delta +V)u=0\) in \(R^ n\)
- Conformal metrics with prescribed scalar curvature
- Regularity for a more general class of quasilinear equations
- Finiteness of the lower spectrum of Schrödinger operators
- Positive solutions of elliptic equations
- On some equivalent properties of sub- and supersolutions in second order quasilinear elliptic equations
- Positive solutions of Yamabe type equations on complete manifolds and applications
- Principal eigenvalues and Sturm comparison via Picone's identity
- Scalar curvature and conformal deformation of hyperbolic space
- Scalar curvature and conformal deformations of noncompact Riemannian manifolds
- Hardy inequalities on non-compact Riemannian manifolds
- Maximum and comparison principles for operators involving the \(p\)-Laplacian
- On the equivalence of two types of oscillation for elliptic operators
- Nonoscillatory elliptic equations
- Positive solutions to \(\Delta u-Vu+Wu^ p=0\) and its parabolic counterpart in noncompact manifolds.
- An exact sequence in \(L^2\)-cohomology
- Volume growth, Green's functions, and parabolicity of ends
- Optimal Hardy weight for second-order elliptic operator: an answer to a problem of Agmon
- Local behavior of solutions of quasi-linear equations
- Vanishing and finiteness results in geometric analysis. A generalization of the Bochner technique
- A Liouville-type theorem for the \(p\)-Laplacian with potential term
- Nonlinear Schrödinger equations with symmetric multi-polar potentials
- Isolated singularities of solutions of quasi-linear equations
- Volume growth and parabolicity
- On the equivalence of stochastic completeness and Liouville and Khas’minskii conditions in linear and nonlinear settings
- C1 + α local regularity of weak solutions of degenerate elliptic equations
- Positive solutions of nonlinear elliptic equations involving critical sobolev exponents
- Positive Solutions of Quasilinear Elliptic Equations on Riemannian Manifolds
- Weighted Poincaré inequality and rigidity of complete manifolds
- Existence and non-existence results for a logistic-type equation on manifolds
- On positive solutions of p-Laplacian-type equations
- On The Dirichletproblem for Quasilinear Equations
- On the spectrum of the laplacian on complete riemannian manifolds
- Remarks on uniqueness results of the first eigenvalue of the p-Laplacian
- The Yamabe problem
- On the Elliptic Equations Δu = K(x)u σ and Δu = K(x)e 2u
- Boundary regularity for solutions of degenerate elliptic equations
- 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
- A Picone's identity for the p-Laplacian and applications
- Nonexistence and uniqueness of positive solutions of Yamabe type equations on nonpositively curved manifolds
- On the elliptic equation Δ𝑢+𝑘𝑢-𝐾𝑢^{𝑝}=0 on complete Riemannian manifolds and their geometric applications
- A unified approach to improved $L^p$ Hardy inequalities with best constants
- Maximum principles on Riemannian manifolds and applications
- Solving the $p$-Laplacian on manifolds
- On some aspects of oscillation theory and geometry
- Yamabe type equations with sign-changing nonlinearities on the Heisenberg group, and the role of Green functions
- Existence of Blowing-up Solutions for a Nonlinear Elliptic Equation with Hardy Potential and Critical Growth
- Role of the fundamental solution in Hardy—Sobolev-type inequalities
- Prescribed scalar curvature problem on complete manifolds.
