Semilinear subelliptic problems with critical growth on Carnot groups

DOI10.1007/S00229-007-0119-XzbMath1146.35028OpenAlexW2044663956MaRDI QIDQ2465209

Annunziata Loiudice

Publication date: 9 January 2008

Published in: Manuscripta Mathematica (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/s00229-007-0119-x

zbMATH Keywords

Carnot groupsAnalysis on Lie groupsSubelliptic Laplacian

Mathematics Subject Classification ID

Degenerate elliptic equations (35J70) Analysis on other specific Lie groups (43A80) Subelliptic equations (35H20)

Related Items (28)

Least-energy nodal solutions of critical Schrödinger-Poisson system on the Heisenberg group ⋮ Existence of nontrivial solutions for critical Kirchhoff-Poisson systems in the Heisenberg group ⋮ \(L^p\)-weak regularity and asymptotic behavior of solutions for critical equations with singular potentials on Carnot groups ⋮ Critical nonlocal Schrödinger-Poisson system on the Heisenberg group ⋮ An integral type Brezis-Nirenberg problem on the Heisenberg group ⋮ Nonlinear elliptic equations on Carnot groups ⋮ A Schrödinger-Poisson system with the critical growth on the first Heisenberg group ⋮ Existence and multiplicity of positive solutions to sub-elliptic systems with multiple critical exponents on Carnot groups ⋮ Compact embeddings, eigenvalue problems, and subelliptic Brezis-Nirenberg equations involving singularity on stratified Lie groups ⋮ On the nonlocal Schrödinger‐poisson type system in the Heisenberg group ⋮ A Brézis-Nirenberg type problem for a class of degenerate elliptic problems involving the Grushin operator ⋮ Nontrivial solutions to boundary value problems for semilinear strongly degenerate elliptic differential equations ⋮ Unnamed Item ⋮ Critical growth problems with singular nonlinearities on Carnot groups ⋮ Yamabe-type equations on Carnot groups ⋮ Dirichlet problem for a class of nonlinear degenerate elliptic operators with critical growth and logarithmic perturbation ⋮ Sub-elliptic systems involving critical Hardy-Sobolev exponents and sign-changing weight functions on Carnot groups ⋮ Local behavior of solutions to subelliptic problems with Hardy potential on Carnot groups ⋮ Subelliptic and parametric equations on Carnot groups ⋮ Optimal decay of \(p\)-Sobolev extremals on Carnot groups ⋮ Critical polyharmonic problems with singular nonlinearities ⋮ The Schrödinger-Poisson type system involving a critical nonlinearity on the first Heisenberg group ⋮ Asymptotic behaviour of solutions for a class of degenerate elliptic critical problems ⋮ Existence and nonexistence results for Kohn Laplacian with Hardy-Littlewood-Sobolev critical exponents ⋮ Critical problems with Hardy potential on stratified Lie groups ⋮ Critical equations with Hardy terms in the Heisenberg group ⋮ A Multiplicity Result for a Non-Homogeneous Subelliptic Problem with Sobolev Exponent ⋮ Entire solutions for some critical equations in the Heisenberg group

Cites Work

• Unnamed Item
• Unnamed Item
• The concentration-compactness principle in the calculus of variations. The limit case. I
• Bifurcation and multiplicity results for nonlinear elliptic problems involving critical Sobolev exponents
• An existence result for nonliner elliptic problems involving critical Sobolev exponent
• Subelliptic estimates and function spaces on nilpotent Lie groups
• A non-existence theorem for a semilinear Dirichlet problem involving critical exponent on halfspaces of the Heisenberg group
• Lower-order perturbations of critical growth nonlinearities in semilinear elliptic equations
• Nonlinear Liouville theorems for some critical problems on \(H\)-type groups.
• Regularity near the characteristic set in the nonlinear Dirichlet problem and conformal geometry of sub-Laplacians on Carnot groups.
• Symmetry properties of positive entire solutions of Yamabe-type equations on groups of Heisenberg type
• A multiplicity result for a degenerate elliptic equation with critical growth on noncontractible domains
• Semilinear Dirichlet problem involving critical exponent for the Kohn Laplacian
• Principe du maximum, inégalité de Harnack et unicité du problème de Cauchy pour les opérateurs elliptiques dégénérées
• Positive solutions of nonlinear elliptic equations involving critical sobolev exponents
• Abstract critical point theorems and applications to some nonlinear problems with “strong” resonance at infinity
• Extremals for the Sobolev Inequality on the Heisenberg Group and the CR Yamabe Problem
• Non-existence results for semilinear kohn-laplace equations in unbounded domains
• Critical semilinear equations on the Heisenberg group: the effect of the topology of the domain

This page was built for publication: Semilinear subelliptic problems with critical growth on Carnot groups