Uniqueness and asymptotic behavior of solutions of a biharmonic equation with supercritical exponent

DOI10.3934/dcds.2019109zbMath1416.35120OpenAlexW2909216859WikidataQ128530330 ScholiaQ128530330MaRDI QIDQ1735351

Zongming Guo, XiaoHong Guan, Yong-Gang Zhao

Publication date: 28 March 2019

Published in: Discrete and Continuous Dynamical Systems (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.3934/dcds.2019109

zbMATH Keywords

biharmonic equationpositive radial solutionsupercritical exponent

Mathematics Subject Classification ID

Existence problems for PDEs: global existence, local existence, non-existence (35A01) Positive solutions to PDEs (35B09) Semilinear elliptic equations with Laplacian, bi-Laplacian or poly-Laplacian (35J91) Uniqueness problems for PDEs: global uniqueness, local uniqueness, non-uniqueness (35A02)

Related Items (4)

A Mathematical Analysis Method for Bending Problem of Clamped Shallow Spherical Shell on Elastic Foundation ⋮ Unnamed Item ⋮ Liouville type results for semilinear biharmonic problems in exterior domains ⋮ Bôcher-type results for the fourth and higher order equations on singular manifolds with conical metrics

Cites Work

• Unnamed Item
• Unnamed Item
• Unnamed Item
• Nonexistence and uniqueness for biharmonic problems with supercritical growth and domain geometry.
• On stable solutions of the biharmonic problem with polynomial growth
• Singular radial entire solutions and weak solutions with prescribed singular set for a biharmonic equation
• Bessel pairs and optimal Hardy and Hardy-Rellich inequalities
• Existence and stability of entire solutions to a semilinear fourth order elliptic problem
• Supercritical biharmonic equations with power-type nonlinearity
• Multiplicity of solutions for a fourth order equation with power-type nonlinearity
• A classification of solutions of a conformally invariant fourth order equation in \(\mathbb{R}^n\)
• Existence and nonexistence results for critical growth biharmonic elliptic equations
• On a nonlinear fourth-order elliptic equation involving the critical Sobolev exponent
• Radial symmetry of entire solutions of a bi-harmonic equation with exponential nonlinearity
• Asymptotic behaviour of the Kazdan-Warner solution in the annulus
• Liouville theorems for stable solutions of biharmonic problem
• Further study of entire radial solutions of a biharmonic equation with exponential nonlinearity
• A monotonicity formula and a Liouville-type theorem for a fourth order supercritical problem
• Radial entire solutions for supercritical biharmonic equations
• Supercritical elliptic problems in domains with small holes
• Qualitative properties of entire radial solutions for a biharmonic equation with supercritical nonlinearity
• Optimal weighted Hardy-Rellich inequalities on H ² ∩ H ₀ ¹
• Stability and intersection properties of solutions to the nonlinear biharmonic equation
• Supercritical biharmonic elliptic problems in domains with small holes
• On a nonlinear elliptic equation involving the critical sobolev exponent: The effect of the topology of the domain
• A rellich type identity and applications
• Uniqueness Theorems for Some Fourth-Order Elliptic Equations
• Functional Inequalities: New Perspectives and New Applications
• Embeddings of weighted Sobolev spaces and a weighted fourth-order elliptic equation
• A Semilinear Fourth Order Elliptic Problem with Exponential Nonlinearity

This page was built for publication: Uniqueness and asymptotic behavior of solutions of a biharmonic equation with supercritical exponent