Non-existence and uniqueness results for supercritical semilinear elliptic equations
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Publication:625070
DOI10.1007/s00023-009-0016-9zbMath1214.35026arXiv0901.0224OpenAlexW2167717527MaRDI QIDQ625070
Jean Dolbeault, Robert Stańczy
Publication date: 14 February 2011
Published in: Annales Henri Poincaré (Search for Journal in Brave)
Full work available at URL: https://arxiv.org/abs/0901.0224
Variational methods for second-order elliptic equations (35J20) Semilinear elliptic equations (35J61) Uniqueness problems for PDEs: global uniqueness, local uniqueness, non-uniqueness (35A02)
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Cites Work
- Free energy and self-interacting particles
- Nonexistence and uniqueness in semilinear elliptic systems
- A construction of singular solutions for a semilinear elliptic equation using asymptotic analysis
- Nonlinear diffusion as limit of kinetic equations with relaxation collision kernels
- Steady states for a system describing self-gravitating Fermi-Dirac particles.
- Quasiconvexity and uniqueness of equilibrium solutions in nonlinear elasticity
- Symmetry and related properties via the maximum principle
- A special class of stationary flows for two-dimensional Euler equations: A statistical mechanics description
- Nonlinear elliptic equations on compact Riemannian manifolds and asymptotics of Emden equations
- Global analysis for a two-dimensional elliptic eigenvalue problem with the exponential nonlinearity
- Some continuation and variational methods for positive solutions of nonlinear elliptic eigenvalue problems
- Exact multiplicity of positive solutions for a class of semilinear problems
- Superlinear indefinite elliptic problems and Pohozyaev type identities
- Poincaré's inequality and global solutions of a nonlinear parabolic equation
- Uniqueness theorems for positive radial solutions of quasilinear elliptic equations in a ball
- Pohozaev obstructions on non-starlike domains
- Uniqueness of solutions for some elliptic equations and systems in nearly star-shaped domains
- Classification of the solutions of semilinear elliptic problems in a ball
- Applications of variational identities to quasilinear elliptic differential equations
- Global solution branches for \(p\)-Laplacian boundary value problems
- Exact multiplicity of positive solutions for a class of semilinear problem. II
- Solutions of semilinear elliptic equations with one isolated singularity.
- Statistical mechanics of the \(N\)-point vortex system with random intensities on a bounded domain
- Some constancy results for nematic liquid crystals and harmonic maps
- A special class of stationary flows for two-dimensional Euler equations: A statistical mechanics description. II
- Multiple bubbling for the exponential nonlinearity in the slightly supercritical case
- On an evolution system describing self-gravitating Fermi-Dirac particles
- On some modes of convergence in spaces with the weak Banach-Saks property
- Some global results for nonlinear eigenvalue problems
- Quasilinear Dirichlet problems driven by positive sources
- Darstellung der Eigenwerte von \(\Delta u+\lambda u=0\) durch ein Randintegral
- Uniqueness of ground states for quasilinear elliptic equations
- Self-attracting Fermi-Dirac particles in canonical and microcanonical setting
- On Some Singular Solutions Of The Equations
- Positive solutions of nonlinear elliptic equations involving critical sobolev exponents
- The role of Onofri type inequalities in the symmetry properties of extremals for Caffarelli-Kohn-Nirenberg inequalities, in two space dimensions
- Geometry of phase space and solutions of semilinear elliptic equations in a ball
- Sur les états d'équilibre pour les densités électroniques dans les plasmas
- Geometry of unbounded domains,poincaré inequalities and stability in semilinear parabolic equations
- Solutions of semilinear elliptic equations with many isolated singularities: the unstable case
- Existence and nonexistence of solutions for a model of gravitational interaction of particles, I
- A class of nonlocal parabolic problems occurring in statistical mechanics
- On the Existence of Positive Solutions of Semilinear Elliptic Equations
- Existence and nonexistence of solutions for a model of gravitational interaction of particles, II
- The existence of equilibria of many-particle systems
- Some problems in the theory of quasilinear equations
- Embedding Theorems and Quasi-Linear Elliptic Boundary Value Problems for Unbounded Domains
- On singular limits of mean-field equations.
- Entropy dissipation methods for degenerate parabolic problems and generalized Sobolev inequalities
- Uniqueness for semilinear elliptic problems: Supercritical growth and domain geometry
- The Brézis-Nirenberg problem on \(\mathbb{S}^3\)
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- Unnamed Item
- Unnamed Item
- Unnamed Item
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