Multiple solutions of a critical polyharmonic equation
From MaRDI portal
Publication:4810852
DOI10.1515/crll.2004.037zbMath1071.35041OpenAlexW2026482567MaRDI QIDQ4810852
Matthias Schneider, Tobias Weth, Thomas J. Bartsch
Publication date: 17 August 2004
Published in: Journal für die reine und angewandte Mathematik (Crelles Journal) (Search for Journal in Brave)
Full work available at URL: https://doi.org/10.1515/crll.2004.037
Critical exponents in context of PDEs (35B33) Nonlinear elliptic equations (35J60) Variational methods for higher-order elliptic equations (35J35)
Related Items
Weighted Sobolev-type embedding theorems for functions with symmetries ⋮ Energy bounds for entire nodal solutions of autonomous superlinear equations ⋮ The prescribed scalar curvature problem for polyharmonic operator ⋮ New existence for the higher order prescribed curvature problem ⋮ Periodic solution for higher order prescribed curvature problem in a strip ⋮ Non-radial solutions for higher order Hénon-type equation with critical exponent ⋮ Infinitely many solutions for the prescribed curvature problem of polyharmonic operator ⋮ Existence and properties of bubbling solutions for a critical nonlinear elliptic equation ⋮ Radial solutions of a polyharmonic equation with power nonlinearity ⋮ Equivariant solutions to the optimal partition problem for the prescribed \(Q\)-curvature equation ⋮ Elliptic system with some singular nonlinearity ⋮ Multiple nontrivial solutions for a class of biharmonic elliptic equations with Sobolev critical exponent ⋮ Non-radial solutions of a supercritical equation in expanding domains: the limit case ⋮ An upper bound for the least energy of a nodal solution to the Yamabe equation on the sphere ⋮ Infinitely many sign-changing solutions to a conformally invariant integral equation on \(\mathbb{R}^n\) ⋮ Existence and convergence of solutions to fractional pure critical exponent problems ⋮ Divergence symmetries of semilinear polyharmonic equations involving critical nonlinearities ⋮ Entire nodal solutions to the critical Lane-Emden system ⋮ Critical polyharmonic systems and optimal partitions ⋮ Nodal solutions for the fractional Yamabe problem on Heisenberg groups ⋮ Construction of solutions for the polyharmonic equation via local Pohozaev identities ⋮ On nontrivial solutions of critical polyharmonic elliptic systems ⋮ Bubble solutions for a supercritical polyharmonic Hénon-type equation ⋮ A Biharmonic Equation in ℜ4 Involving Nonlinearities with Subcritical Exponential Growth ⋮ Geometrically distinct solutions given by symmetries of variational problems with the O(N)-symmetry ⋮ Existence and nonexistence results for critical growth polyharmonic elliptic systems ⋮ Yamabe problem in the presence of singular Riemannian foliations ⋮ Non-degeneracy of bubble solutions for higher order prescribed curvature problem ⋮ Infinitely many sign-changing solutions of a critical fractional equation
Cites Work
- Unnamed Item
- Sharp Sobolev inequalities on the sphere and the Moser-Trudinger inequality
- The principle of symmetric criticality
- Sharp constants in the Hardy-Littlewood-Sobolev and related inequalities
- A global compactness result for elliptic boundary value problems involving limiting nonlinearities
- On a conformally invariant elliptic equation on \(R^ n\)
- Group representations arising from Lorentz conformal geometry
- Symmetry and related properties via the maximum principle
- Existence and multiplicity of nodal solutions for nonlinear elliptic equations with critical Sobolev growth
- Positive solutions to semilinear polyharmonic Dirichlet problems involving critical Sobolev exponents
- Positivity for equations involving polyharmonic operators with Dirichlet boundary conditions
- Sobolev spaces in the presence of symmetries
- Paneitz-type operators and applications
- Critical exponents and critical dimensions of polyharmonic operators
- The best sobolev constant
- Infinitely many solutions for some nonlinear elliptic problems in symmetrical domains
- Existence and regularity of weak solutions to the Dirichletproblem for semilinear elliptic systems of higher order.