Nonradial solutions for a conformally invariant fourth order equation in \(\mathbb {R}^4\)
From MaRDI portal
Publication:927298
DOI10.1007/s00526-007-0145-2zbMath1143.35050OpenAlexW2079783478WikidataQ115387680 ScholiaQ115387680MaRDI QIDQ927298
Publication date: 4 June 2008
Published in: Calculus of Variations and Partial Differential Equations (Search for Journal in Brave)
Full work available at URL: https://doi.org/10.1007/s00526-007-0145-2
Singular perturbations in context of PDEs (35B25) Nonlinear elliptic equations (35J60) Asymptotic expansions of solutions to PDEs (35C20) Relations of PDEs with special manifold structures (Riemannian, Finsler, etc.) (58J60) Variational methods for higher-order elliptic equations (35J35)
Related Items (34)
The fourth order elliptic problem with exponential nonlinearity ⋮ Existence of infinitely many spike solutions for a critical Hénon type biharmonic equation ⋮ Classification of solutions to the higher order Liouville's equation on \({\mathbb{R}^{2m}}\) ⋮ Blow up solutions for a 4-dimensional Emden-Fowler system of Liouville type ⋮ Local and Nonlocal Singular Liouville Equations in Euclidean Spaces ⋮ Classification of solutions to a system of \(n^{\mathrm{th}}\) order equations on \(\mathbb{R}^n\) ⋮ The \(\operatorname{SU}(3)\) Toda system with multiple singular sources ⋮ Existence and asymptotic behavior of non-normal conformal metrics on ℝ4 with sign-changing Q-curvature ⋮ Large blow-up sets for the prescribed Q-curvature equation in the Euclidean space ⋮ Singular metrics of constant negative \(Q\)-curvature in Euclidean spaces ⋮ Nonradial singular metrics of constant \(Q\)-curvature ⋮ Singular limit solutions for a four‐dimensional semilinear elliptic Kuramoto–Sivashinsky system in some general case ⋮ The Gel'fand problem for the biharmonic operator ⋮ Further study of entire radial solutions of a biharmonic equation with exponential nonlinearity ⋮ Remarks on Entire Solutions for Two Fourth-Order Elliptic Problems ⋮ Solutions of Liouville equations with non-trivial profile in dimensions 2 and 4 ⋮ Existence and stability of entire solutions to a semilinear fourth order elliptic problem ⋮ Asymptotic behavior of solutions for some elliptic equations in exterior domains ⋮ Conformal metrics on \(\mathbb{R}^{2m}\) with constant \(Q\)-curvature, prescribed volume and asymptotic behavior ⋮ Unnamed Item ⋮ Fractional Adams-Moser-Trudinger type inequalities ⋮ Nonexistence of solutions to singular Q-curvature equations ⋮ Conformally Euclidean metrics on \(\mathbb{R}^n\) with arbitrary total Q-curvature ⋮ Radial symmetry of entire solutions of a bi-harmonic equation with exponential nonlinearity ⋮ Existence and asymptotics for solutions of a non-local Q-curvature equation in dimension three ⋮ Conformal metrics in \(\mathbb {R}^{2m}\) with constant \(Q\)-curvature and arbitrary volume ⋮ Existence of stable solutions to \((-\Delta)^m u = e^u\) in \(\mathbb{R}^N\) with \(m\geq 3\) and \(N>2m\) ⋮ Constant \(Q\)-curvature metrics near the hyperbolic metric ⋮ Higher order conformally invariant equations in \( \mathbb{R}^3 \) with prescribed volume ⋮ Concentration phenomena to a higher order Liouville equation ⋮ Non-radial solutions to a bi-harmonic equation with negative exponent ⋮ Blow-up in coupled solutions for a \(4\)-dimensional semilinear elliptic Kuramoto-Sivashinsky system ⋮ Constant 𝑄-curvature metrics with a singularity ⋮ Existence and stability properties of entire solutions to the polyharmonic equation \((-\Delta)^{m}u=e^{u}\) for any \(m\geq 1\)
Cites Work
- Unnamed Item
- Classification of solutions of some nonlinear elliptic equations
- Classification of solutions of higher order conformally invariant equations
- On uniqueness of solutions of \(n\)-th order differential equations in conformal geometry
- The zeta functional determinants on manifolds with boundary. I: The formula
- A classification of solutions of a conformally invariant fourth order equation in \(\mathbb{R}^n\)
- A note on a class of higher order conformally covariant equations
- Extremal metrics of zeta function determinants on 4-manifolds
- Critical exponents and critical dimensions of polyharmonic operators
- The behavior of the laplacian on weighted sobolev spaces
This page was built for publication: Nonradial solutions for a conformally invariant fourth order equation in \(\mathbb {R}^4\)
