Ground states of bi-harmonic equations with critical exponential growth involving constant and trapping potentials

DOI10.1007/s00526-020-01831-4zbMath1467.46033arXiv1909.01952OpenAlexW3092190859WikidataQ115387057 ScholiaQ115387057MaRDI QIDQ2217790

Guozhen Lu, Maochun Zhu, Lu Chen

Publication date: 14 January 2021

Published in: Calculus of Variations and Partial Differential Equations (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1909.01952

zbMATH Keywords

bi-harmonic equationground-state solutionsnonsymmetric trapping potentialRabinowitz type trapping potential

Mathematics Subject Classification ID

Sobolev spaces and other spaces of ``smooth functions, embedding theorems, trace theorems (46E35) Inequalities involving derivatives and differential and integral operators (26D10) Semilinear elliptic equations with Laplacian, bi-Laplacian or poly-Laplacian (35J91)

Related Items (10)

Existence of extremals for Trudinger-Moser inequalities involved with a trapping potential ⋮ Existence of ground state solutions for weighted biharmonic problem involving non linear exponential growth ⋮ 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 ⋮ Existence solutions for a weighted biharmonic equation with critical exponential growth ⋮ Ground state solution for a weighted fourth-order Schrödinger equation with exponential growth nonlinearity ⋮ Biharmonic Kirchhoff type elliptic systems with the singular exponential nonlinearities in \(\mathbb{R}^4\) ⋮ Multiple solutions for a singular nonhomogenous biharmonic equation in Heisenberg group ⋮ Sharp Trudinger-Moser inequality and ground state solutions to quasi-linear Schrödinger equations with degenerate potentials in \(\mathbb{R}^n\) ⋮ A critical Trudinger-Moser inequality involving a degenerate potential and nonlinear Schrödinger equations

Cites Work

• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Sharp Moser-Trudinger inequalities on hyperbolic spaces with exact growth condition
• 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 \(m\)
• Polyharmonic equations with critical exponential growth in the whole space \(\mathbb{R}^{n}\)
• Existence of a ground state solution for a nonlinear scalar field equation with critical growth
• Existence of positive solutions to quasi-linear elliptic equations with exponential growth in the whole Euclidean space
• Existence and multiplicity of solutions to equations of \(N\)-Laplacian type with critical exponential growth in \(\mathbb R^N\)
• The concentration-compactness principle in the calculus of variations. The locally compact case. I
• Perturbation methods and semilinear elliptic problems on \(\mathbb R^n\)
• Ground states of \(-\Delta u=f(u)\) and the Emden-Fowler equation
• Ground states and Dirichlet problems for \(-\Delta u=f(u)\) in \(R^ 2\)
• A sharp inequality of J. Moser for higher order derivatives
• On a class of nonlinear Schrödinger equations
• Introduction à la théorie des points critiques et applications aux problèmes elliptiques
• Elliptic equations in \(R^ 2\) with nonlinearities in the critical growth range
• Semiclassical states of nonlinear Schrödinger equations
• Fourier analysis and optimal Hardy-Adams inequalities on hyperbolic spaces of any even dimension
• Concentration-compactness principle for Trudinger-Moser inequalities on Heisenberg groups and existence of ground state solutions
• Sharpened Adams inequality and ground state solutions to the bi-Laplacian equation in \(\mathbb{R}^4\)
• Equivalence of critical and subcritical sharp Trudinger-Moser-Adams inequalities
• Sharp Moser-Trudinger inequality on the Heisenberg group at the critical case and applications
• A sharp Trudinger-Moser type inequality for unbounded domains in \(\mathbb R^2\)
• On concentration of positive bound states of nonlinear Schrödinger equations
• \(N\)-Laplacian equations in \(\mathbb{R}^N\) with critical growth
• On the existence of positive entire solutions of a semilinear elliptic equation
• On critical cases of Sobolev's inequalities
• Min-max level estimate for a singular quasilinear polyharmonic equation in \(\mathbb R^{2m}\)
• A biharmonic equation in \(\mathbb{R}^4\) involving nonlinearities with critical exponential growth
• Dual variational methods in critical point theory and applications
• Sharp singular Trudinger-Moser inequalities under different norms
• Sharp weighted Trudinger-Moser-Adams inequalities on the whole space and the existence of their extremals
• Existence and nonexistence of extremal functions for sharp Trudinger-Moser inequalities
• Trudinger-Moser inequality on the whole plane with the exact growth condition
• On multiplicity and concentration of positive solutions for a class of quasilinear problems with critical exponential growth in \(\mathbb R^{N}\)
• Sharp Hardy-Adams inequalities for bi-Laplacian on hyperbolic space of dimension four
• 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
• Ground States for Elliptic Equations in $\pmb{\mathbb{R}}^{2}$ with Exponential Critical Growth
• Positive solutions of nonlinear elliptic equations involving critical sobolev exponents
• Upper bound of the best constant of the Trudinger-Moser inequality and its application to the Gagliardo-Nirenberg inequality
• Trudinger-Moser Inequalities with the Exact Growth Condition in ℝ^Nand Applications
• Best Constants for Adams’ Inequalities with the Exact Growth Condition in ℝⁿ
• On nonlinear Schrödinger equations with totally degenerate potentials
• Higher order Adams’ inequality with the exact growth condition
• Sharp Adams-type inequalities in ℝⁿ
• Trudinger type inequalities in $\mathbf {R}^N$ and their best exponents
• Sharp Adams and Hardy-Adams inequalities of any fractional order on hyperbolic spaces of all dimensions
• Paneitz operators on hyperbolic spaces and high order Hardy-Sobolev-Maz'ya inequalities on half spaces
• A sharp Trudinger-Moser type inequality for unbounded domains in $\mathbb{R}^n$
• Adams' Inequality with the Exact Growth Condition in ℝ⁴
• Multiplicity results for some nonlinear Schrödinger equations with potentials
• On interacting bumps of semi-classical states of nonlinear Schrödinger equations.

This page was built for publication: Ground states of bi-harmonic equations with critical exponential growth involving constant and trapping potentials