On the Kirchhoff equation with prescribed mass and general nonlinearities

DOI10.3934/dcdss.2023160arXiv2112.10293OpenAlexW4386452369MaRDI QIDQ6149442

Yimin Zhang, Jian Jun Zhang, Xiaoyu Zeng, Xue Xiu Zhong

Publication date: 5 February 2024

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

Full work available at URL: https://arxiv.org/abs/2112.10293

zbMATH Keywords

existencemultiplicitynon-existenceKirchhoff-type equation

Mathematics Subject Classification ID

Existence problems for PDEs: global existence, local existence, non-existence (35A01) Quasilinear elliptic equations (35J62)

Cites Work

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• The mass concentration phenomenon for \(L^2\)-critical constrained problems related to Kirchhoff equations
• Existence and asymptotic behavior of high energy normalized solutions for the Kirchhoff type equations in \(\mathbb{R}^3\)
• Concentrating bounded states for a class of singularly perturbed Kirchhoff type equations with a general nonlinearity
• An autonomous Kirchhoff-type equation with general nonlinearity in \(\mathbb{R}^N\)
• Existence and concentration result for the Kirchhoff type equations with general nonlinearities
• Multiple positive solutions for Kirchhoff type of problems with singularity and critical exponents
• Existence of a positive solution to Kirchhoff-type problems without compactness conditions
• Multiplicity and concentration of positive solutions for a Kirchhoff type problem with critical growth
• The elliptic Kirchhoff equation in \(\mathbb {R}^{N}\) perturbed by a local nonlinearity.
• The existence of normalized solutions for \(L^2\)-critical constrained problems related to Kirchhoff equations
• A natural constraint approach to normalized solutions of nonlinear Schrödinger equations and systems
• Existence and concentration behavior of positive solutions for a Kirchhoff equation in \(\mathbb R^3\)
• Existence and asymptotic behavior of nodal solutions for the Kirchhoff-type problems in \(\mathbb{R}^3\)
• Nonlinear scalar field equations. II: Existence of infinitely many solutions
• Nonlinear scalar field equations. I: Existence of a ground state
• The concentration-compactness principle in the calculus of variations. The locally compact case. I
• The concentration-compactness principle in the calculus of variations. The locally compact case. II
• Blow-up solutions for a Kirchhoff type elliptic equation with trapping potential
• Normalized solutions of nonlinear Schrödinger equations
• Multiple solutions for the nonhomogeneous Kirchhoff equation on \(\mathbb R^N\)
• A mass supercritical problem revisited
• Normalized ground states of the nonlinear Schrödinger equation with at least mass critical growth
• A study on the critical Kirchhoff problem in high-dimensional space
• On global minimizers for a mass constrained problem
• Normalized solutions for Schrödinger equations with critical Sobolev exponent and mixed nonlinearities
• Multiple normalized solutions for a Sobolev critical Schrödinger equation
• A note on deformation argument for \(L^2\) normalized solutions of nonlinear Schrödinger equations and systems
• Infinitely many solutions for Kirchhoff problems with lack of compactness
• Normalized ground states for the NLS equation with combined nonlinearities: the Sobolev critical case
• Normalized ground states for the NLS equation with combined nonlinearities
• Constraint minimizers of Kirchhoff-Schrödinger energy functionals with \(L^2\)-subcritical perturbation
• Existence and asymptotic behavior of minimizers for the Kirchhoff functional with periodic potentials
• Positive solutions of Kirchhoff type elliptic equations involving a critical Sobolev exponent
• On the normalized ground states of second order PDE's with mixed power non-linearities
• The existence of constrained minimizers for a class of nonlinear Kirchhoff-Schrödinger equations with doubly critical exponents in dimension four
• Sign-changing solutions for a class of Kirchhoff-type problem in bounded domains
• Ground states for Kirchhoff equations without compact condition
• Existence and uniqueness of normalized solutions for the Kirchhoff equation
• Stable standing waves of nonlinear Schrödinger equations with a general nonlinear term
• Existence of positive ground state solutions for the nonlinear Kirchhoff type equations in \(\mathbb{R}^3\)
• Positive solutions for a quasilinear elliptic equation of Kirchhoff type
• Existence and blow up behavior of positive normalized solution to the Kirchhoff equation with general nonlinearities: mass super-critical case
• Concentrating Bound States for Kirchhoff Type Problems in ℝ³ Involving Critical Sobolev Exponents
• Existence of solutions with prescribed norm for semilinear elliptic equations
• The sharp existence of constrained minimizers for a class of nonlinear Kirchhoff equations
• A Note on a Mountain Pass Characterization of Least Energy Solutions
• Bifurcation for Dirichlet Problems Without Eigenvalues
• A remark on least energy solutions in $\mathbf {R}^N$
• Normalized ground states for Kirchhoff equations in R3 with a critical nonlinearity
• Normalized solutions to a class of Kirchhoff equations with Sobolev critical exponent
• Multi‐peak solutions of Kirchhoff equations involving subcritical or critical Sobolev exponents
• Nonradial normalized solutions for nonlinear scalar field equations
• A note on the elliptic Kirchhoff equation in ℝ^Nperturbed by a local nonlinearity