Singularity and decay estimates in superlinear problems via Liouville-type theorems. I: Elliptic equations and systems

DOI10.1215/S0012-7094-07-13935-8zbMath1146.35038OpenAlexW2088616362MaRDI QIDQ2382011

Pavol Quittner, Philippe Souplet, Peter Poláčik

Publication date: 27 September 2007

Published in: Duke Mathematical Journal (Search for Journal in Brave)

Full work available at URL: https://projecteuclid.org/euclid.dmj/1187916270

zbMATH Keywords

Liouville-type theoremsuperlinear problemLane-Emden type systemssingularity and decay estimates

Mathematics Subject Classification ID

Related Items (only showing first 100 items - show all)

Liouville type theorem for critical order Hénon-Lane-Emden type equations on a half space and its applications ⋮ A priori bounds and existence of positive solutions of an elliptic system of Kirchhoff type in three or four space dimensions ⋮ Universal bounds and blow-up estimates for a reaction-diffusion system ⋮ Fractional Hardy-Hénon equations on exterior domains ⋮ Stable and finite Morse index solutions of a nonlinear elliptic system ⋮ Singularity and decay estimates for the conformal \(k\)-hessian equation via Liouville-type theorems ⋮ Liouville type theorems for systems of elliptic differential inequalities on Riemannian manifolds ⋮ Liouville-type theorem for a nonlinear degenerate parabolic system of inequalities ⋮ On the Hardy-Littlewood-Sobolev type systems ⋮ A Liouville-type theorem for the 3-dimensional parabolic Gross-Pitaevskii and related systems ⋮ Symmetry and nonexistence of positive solutions for fractional systems ⋮ Existence and non-existence results for variational higher order elliptic systems ⋮ On existence and nonexistence of positive solutions of an elliptic system with coupled terms ⋮ Existence and nonexistence of a positive solution of the Lane-Emden equation having a boundary singularity: the subcritical case ⋮ Singularity and blow-up estimates via Liouville-type theorems for Hardy-Hénon parabolic equations ⋮ Nonexistence of positive solutions of an integral system with weights ⋮ Liouville type theorem to an integral system in the half-space ⋮ Blow-up rate estimates and Liouville type theorems for a semilinear heat equation with weighted source ⋮ Nonexistence of positive supersolutions to some nonlinear elliptic problems ⋮ A priori estimates and application to the symmetry of solutions for critical \(p\)-Laplace equations ⋮ Quantitative local bounds for subcritical semilinear elliptic equations ⋮ Liouville-type theorems for a quasilinear elliptic equation of the Hénon-type ⋮ Liouville theorems for the Navier-Stokes equations and applications ⋮ Isolated boundary singularities of semilinear elliptic equations ⋮ Optimal Liouville-type theorems for noncooperative elliptic Schrödinger systems and applications ⋮ Monotonicity and radial symmetry results for Schrödinger systems with fractional diffusion ⋮ Asymptotic and optimal Liouville properties for Wolff type integral systems ⋮ Liouville theorems, universal estimates and periodic solutions for cooperative parabolic Lotka-Volterra systems ⋮ Symmetry of solutions for a fractional system ⋮ Liouville-type theorems for semilinear elliptic systems ⋮ Liouville type theorems for elliptic equations with gradient terms ⋮ A universal bound for radial solutions of the quasilinear parabolic equation with \(p\)-Laplace operator ⋮ A priori estimates, existence and non-existence of positive solutions of generalized mean curvature equations ⋮ Asymptotic radial symmetry and growth estimates of positive solutions to weighted Hardy-Littlewood-Sobolev system of integral equations ⋮ A Liouville theorem for the subcritical Lane-Emden system ⋮ A priori bounds and existence result of positive solutions for fractional Laplacian systems ⋮ Liouville-type theorems and bounds of solutions of Hardy-Hénon equations ⋮ A fourth order elliptic equation with a singular nonlinearity ⋮ Optimal Liouville-type theorems for a parabolic system ⋮ A characterization of fast decaying solutions for quasilinear and Wolff type systems with singular coefficients ⋮ Symmetry breaking via Morse index for equations and systems of Hénon-Schrödinger type ⋮ Local behavior of solutions to fractional Hardy-Hénon equations with isolated singularity ⋮ A Liouville theorem for \(p\)-harmonic functions on exterior domains ⋮ Decay estimates and a vanishing phenomenon for the solutions of critical anisotropic equations ⋮ Liouville theorems for stable solutions of the weighted Lane-Emden system ⋮ Liouville type results for semilinear biharmonic problems in exterior domains ⋮ Symmetry of positive solutions for Hartree type nonlocal Lane-Emden system ⋮ Nonexistence results for a semilinear heat equation with bounded potentials ⋮ On the existence and multiplicity of solutions to fractional Lane-Emden elliptic systems involving measures ⋮ Analysis of an elliptic system with infinitely many solutions ⋮ Semilinear elliptic system with boundary singularity ⋮ Further study of a weighted elliptic equation ⋮ Existence of solutions to higher order Lane-Emden type systems ⋮ On the sixth-order Joseph-Lundgren exponent ⋮ Proof of the Hénon-Lane-Emden conjecture in \(\mathbb{R}^3\) ⋮ Liouville results for \(m\)-Laplace equations in half-space and strips with mixed boundary value conditions and finite Morse index ⋮ Sharp pointwise estimates for weighted critical \(p\)-Laplace equations ⋮ Monotonicity and symmetry of nonnegative solutions to \(-\Delta u=f(u)\) in half-planes and strips ⋮ Liouville-type theorems for nonlinear degenerate parabolic equation ⋮ Existence of solutions to nonlinear, subcritical higher order elliptic Dirichlet problems ⋮ Exhaustive existence and non-existence results for some prototype polyharmonic equations in the whole space ⋮ Partial regularity of finite Morse index solutions to the Lane-Emden equation ⋮ Threshold results for semilinear parabolic systems ⋮ A monotonicity theorem and its applications to weighted elliptic equations ⋮ A priori bounds versus multiple existence of positive solutions for a nonlinear Schrödinger system ⋮ The Toda system and multiple-end solutions of autonomous planar elliptic problems ⋮ Sharp existence criteria for positive solutions of Hardy-Sobolev type systems ⋮ A note on the Ambrosetti-Rabinowitz condition for an elliptic system ⋮ Liouville-type theorems and decay estimates for solutions to higher order elliptic equations ⋮ Liouville theorems for elliptic systems and applications ⋮ Study of the existence of supersolutions for nonlocal equations with gradient terms ⋮ A Liouville theorem for a class of fractional systems in \(\mathbb{R}_+^n\) ⋮ Liouville type theorems for fractional and higher-order fractional systems ⋮ On problems with weighted elliptic operator and general growth nonlinearities ⋮ The regularity lifting methods for nonnegative solutions of Lane-Emden system ⋮ Liouville-type theorems and existence results for stable-at-infinity solutions of higher-order \(m\)-polyharmonic problems ⋮ Optimal Liouville theorems for superlinear parabolic problems ⋮ Liouville theorems for elliptic systems with nonlinear gradient terms ⋮ Liouville-type theorems for sign-changing solutions to nonlocal elliptic inequalities and systems with variable-exponent nonlinearities ⋮ Method of scaling spheres for integral and polyharmonic systems ⋮ The local behavior of positive solutions for higher order equation with isolated singularities ⋮ The homogeneous Hénon-Lane-Emden system ⋮ Liouville-type theorem for higher-order Hardy-Hénon system ⋮ Lorentz-Sobolev spaces and systems of Schrödinger equations in \(\mathbb R^N\) ⋮ A Liouville theorem for ancient solutions to a semilinear heat equation and its elliptic counterpart ⋮ The proof of the Lane-Emden conjecture in four space dimensions ⋮ Liouville theorems for nonnegative solutions to Hardy-Hénon type system on a half space ⋮ A priori estimates for solutions of anisotropic elliptic equations ⋮ Finite Morse index solutions of the Hénon Lane-Emden equation ⋮ Regularity and existence of positive solutions for a fractional system ⋮ Nonexistence of positive solutions to \(n\)-th order equations in \(\mathbb{R}^n\) ⋮ A Bahri-Lions theorem revisited ⋮ Liouville type theorems for stable solutions of elliptic system involving the Grushin operator ⋮ Existence and Liouville-type theorems for some indefinite quasilinear elliptic problems with potentials vanishing at infinity ⋮ Existence and Liouville theorems for coupled fractional elliptic system with Stein-Weiss type convolution parts ⋮ Triviality of bounded solutions and gradient estimates for nonlinear \(f\)-heat equations on complete smooth metric measure spaces ⋮ Asymptotic behavior of positive solutions to a nonlinear biharmonic equation near isolated singularities ⋮ Nonexistence of positive solutions for high-order Hardy-Hénon systems on \(\mathbb{R}^n\) ⋮ Classification of finite Morse index solutions to the polyharmonic Hénon equation ⋮ A Liouville-type theorem for higher order elliptic systems of Hénon-Lane-Emden type

This page was built for publication: Singularity and decay estimates in superlinear problems via Liouville-type theorems. I: Elliptic equations and systems