Polyharmonic equations with critical exponential growth in the whole space \(\mathbb{R}^{n}\)

DOI10.3934/dcds.2016.36.577zbMath1323.35046OpenAlexW2336774727MaRDI QIDQ495769

Guozhen Lu, Lam Hoang Nguyen, Ji Guang Bao

Publication date: 15 September 2015

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

Full work available at URL: https://doi.org/10.3934/dcds.2016.36.577

zbMATH Keywords

existenceexponential growthBessel potentialpolyharmonic equationsMoser-Trudinger and Adams inequalitiessymmetry and regularity of solutions

Mathematics Subject Classification ID

Smoothness and regularity of solutions to PDEs (35B65) Critical exponents in context of PDEs (35B33) Biharmonic and polyharmonic equations and functions in higher dimensions (31B30) Variational methods for higher-order elliptic equations (35J35) Positive solutions to PDEs (35B09) Symmetries, invariants, etc. in context of PDEs (35B06) Semilinear elliptic equations with Laplacian, bi-Laplacian or poly-Laplacian (35J91) Harmonic analysis and PDEs (42B37)

Related Items (11)

Trudinger-Moser inequalities in fractional Sobolev-Slobodeckij spaces and multiplicity of weak solutions to the fractional-Laplacian equation ⋮ Moser functions and fractional Moser-Trudinger type inequalities ⋮ Sharpened Adams inequality and ground state solutions to the bi-Laplacian equation in \(\mathbb{R}^4\) ⋮ Least energy solutions to quasilinear subelliptic equations with constant and degenerate potentials on the Heisenberg group ⋮ Existence and non-existence of ground states of bi-harmonic equations involving constant and degenerate Rabinowitz potentials ⋮ Bubbling phenomenon for semilinear Neumann elliptic equations of critical exponential growth ⋮ Ground states of bi-harmonic equations with critical exponential growth involving constant and trapping potentials ⋮ Ground state solutions of polyharmonic equations with potentials of positive low bound ⋮ Adams' type inequality and application to a quasilinear nonhomogeneous equation with singular and vanishing radial potentials in \( \mathbb{R}^4 \) ⋮ On the solvability of a semilinear higher-order elliptic problem for the vector field method in image registration ⋮ Qualitative properties of solutions to an integral system associated with the Bessel potential

Cites Work

• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Existence of nontrivial solutions to polyharmonic equations with subcritical and critical exponential growth
• Sharp Adams type inequalities in Sobolev spaces \(W^{m,\frac{n}{m}}(\mathbb R^n)\) for arbitrary integer \(m\)
• Regularity of solutions for an integral system of Wolff type
• Radial symmetry and regularity of solutions for poly-harmonic Dirichlet problems
• Regularity of solutions to an integral equation associated with Bessel potential
• Existence and multiplicity of solutions to equations of \(N\)-Laplacian type with critical exponential growth in \(\mathbb R^N\)
• Nonlinear scalar field equations. I: Existence of a ground state
• The concentration-compactness principle in the calculus of variations. The limit case. I
• The concentration-compactness principle in the calculus of variations. The limit case. II
• Polyharmonic boundary value problems. Positivity preserving and nonlinear higher order elliptic equations in bounded domains
• On a quasilinear nonhomogeneous elliptic equation with critical growth in \(\mathbb R^N\)
• Ground states and Dirichlet problems for \(-\Delta u=f(u)\) in \(R^ 2\)
• A sharp inequality of J. Moser for higher order derivatives
• Symmetry and related properties via the maximum principle
• Extremal functions for the Trudinger-Moser inequality in 2 dimensions
• Sharp borderline Sobolev inequalities on compact Riemannian manifolds
• Introduction à la théorie des points critiques et applications aux problèmes elliptiques
• Elliptic equations in \(R^ 2\) with nonlinearities in the critical growth range
• On nonlinear perturbations of a periodic elliptic problem in \(\mathbb R^2\) involving critical growth.
• Sharp Moser-Trudinger inequality on the Heisenberg group at the critical case and applications
• A sharp Trudinger-Moser type inequality for unbounded domains in \(\mathbb R^2\)
• Adams' inequality and limiting Sobolev embeddings into Zygmund spaces
• Dual variational methods in critical point theory and applications
• Remarks on the extremal functions for the Moser-Trudinger inequality
• Multiplicity results for a class of semilinear elliptic equations on \(\mathbb{R}^ m\)
• A new approach to sharp Moser-Trudinger and Adams type inequalities: a rearrangement-free argument
• Sharp subcritical Moser-Trudinger inequalities on Heisenberg groups and subelliptic PDEs
• ON REGULARITY OF SOLUTIONS TO AN INTEGRAL SYSTEM ASSOCIATED WITH BESSEL POTENTIALS
• Upper bound of the best constant of the Trudinger-Moser inequality and its application to the Gagliardo-Nirenberg inequality
• Nonsymmetric ground states of symmetric variational problems
• Nontrivial Solution of Semilinear Elliptic Equations with Critical Exponent in R
• Homoclinic type solutions for a semilinear elliptic PDE on ℝⁿ
• Extremal functions for Moser’s inequality
• Sharp Adams-type inequalities in ℝⁿ
• Quasilinear elliptic problems with critical exponents
• A sharp Trudinger-Moser type inequality for unbounded domains in $\mathbb{R}^n$
• Classification of solutions for an integral equation
• Methods in Nonlinear Analysis
• Nonlinear perturbations of a periodic elliptic problem with critical growth.

This page was built for publication: Polyharmonic equations with critical exponential growth in the whole space \(\mathbb{R}^{n}\)