Liouville type theorems, a priori estimates and existence of solutions for sub-critical order Lane-Emden-Hardy equations

DOI10.1007/s11854-022-0207-6zbMath1497.35255OpenAlexW4285042479WikidataQ113899794 ScholiaQ113899794MaRDI QIDQ2164787

Shaolong Peng, Guolin Qin, Wei Dai

Publication date: 17 August 2022

Published in: Journal d'Analyse Mathématique (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/s11854-022-0207-6

zbMATH Keywords

existenceLiouville theoremsLane-Emden-Hardy equations

Mathematics Subject Classification ID

Existence problems for PDEs: global existence, local existence, non-existence (35A01) Higher-order elliptic equations (35J30) Semilinear elliptic equations with Laplacian, bi-Laplacian or poly-Laplacian (35J91) Liouville theorems and Phragmén-Lindelöf theorems in context of PDEs (35B53)

Related Items (7)

On properties of positive solutions to nonlinear tri-harmonic and bi-harmonic equations with negative exponents ⋮ Liouville theorem for Hénon-Hardy systems in the unit ball ⋮ Liouville type theorems for the generalized higher order Choquard-Pekar equation ⋮ Classification of solutions for mixed order conformally system with Hartree-type nonlinearity in ℝn ⋮ Unnamed Item ⋮ Existence and Liouville theorems for coupled fractional elliptic system with Stein-Weiss type convolution parts ⋮ Maximum principles and Liouville results for uniformly elliptic nonlocal Bellman system

Cites Work

• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• A direct method of moving planes for the fractional Laplacian
• A Liouville type theorem for higher order Hardy-Hénon equation in \(\mathbb R^n\)
• A new dynamical approach of Emden-Fowler equations and systems
• Liouville-type theorems and bounds of solutions of Hardy-Hénon equations
• The scalar-curvature problem on the standard three-dimensional sphere
• The proof of the Lane-Emden conjecture in four space dimensions
• Symmetry and related properties via the maximum principle
• A perturbation result in prescribing scalar curvature on \(S^ n\)
• Classification of solutions of some nonlinear elliptic equations
• A priori estimates for solutions to 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
• A priori estimates for prescribing scalar curvature equations
• A classification of solutions of a conformally invariant fourth order equation in \(\mathbb{R}^n\)
• Classification of nonnegative classical solutions to third-order equations
• Regularity and classification of solutions to static Hartree equations involving fractional Laplacians
• Classification of positive solutions to fractional order Hartree equations via a direct method of moving planes
• Prescribing scalar curvature on \(\mathbb{S}^ n\) and related problems. I
• Local behavior of singular positive solutions of semilinear elliptic equations with Sobolev exponent
• Prescribed scalar curvature on the \(n\)-sphere
• Local asymptotic symmetry of singular solutions to nonlinear elliptic equations
• Nonexistence of positive solutions of semilinear elliptic systems in \(\mathbb{R}^ N\)
• Non-existence of positive solutions of Lane-Emden systems
• Asymptotic properties of positive solutions of the Hardy-Sobolev type equations
• Super polyharmonic property of solutions for PDE systems and its applications
• Liouville theorems involving the fractional Laplacian on a half space
• Singularity and decay estimates in superlinear problems via Liouville-type theorems. I: Elliptic equations and systems
• Super poly-harmonic property of solutions for Navier boundary problems on a half space
• On the Hénon-Lane-Emden conjecture
• Asymptotic symmetry and local behavior of semilinear elliptic equations with critical sobolev growth
• A priori bounds for positive solutions of nonlinear elliptic equations
• Global and local behavior of positive solutions of nonlinear elliptic equations
• Uniform estimates and blow–up behavior for solutions of −δ(u)=v(x)e^uin two dimensions
• Classification of Solutions of a Conformally Invariant Third Order Equation in ℝ³
• Classification of nonnegative solutions to a bi-harmonic equation with Hartree type nonlinearity
• Liouville type theorems for Hardy–Hénon equations with concave nonlinearities
• The Fractional Laplacian
• Classification of solutions for an integral equation
• Liouville-type theorems for polyharmonic H\'enon-Lane-Emden system

This page was built for publication: Liouville type theorems, a priori estimates and existence of solutions for sub-critical order Lane-Emden-Hardy equations