The existence of constrained minimizers for a class of nonlinear Kirchhoff-Schrödinger equations with doubly critical exponents in dimension four

DOI10.1016/j.na.2018.12.010zbMath1419.49006OpenAlexW2906728466MaRDI QIDQ2312582

Junping Shi, Xiaocui Hao, Yuhua Li

Publication date: 17 July 2019

Published in: Nonlinear Analysis. Theory, Methods \& Applications. Series A: Theory and Methods (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/j.na.2018.12.010

zbMATH Keywords

critical exponentconstrained minimizationenergy minimizerKirchhoff-Schrödinger equation

Mathematics Subject Classification ID

Existence theories for optimal control problems involving ordinary differential equations (49J15)

Related Items

Normalized solutions of the autonomous Kirchhoff equation with Sobolev critical exponent: Sub- and super-critical cases, Blow-up behavior of \(L^2\)-norm solutions for Kirchhoff equation in a bounded domain, On the Kirchhoff equation with prescribed mass and general nonlinearities, Normalized ground states for the mass-energy doubly critical Kirchhoff equations, Normalized solutions to the mass supercritical Kirchhoff-type equation with non-trapping potential, Normalized solutions to the Kirchhoff equation with potential term: mass super-critical case, Constraint minimizers of Kirchhoff-Schrödinger energy functionals with \(L^2\)-subcritical perturbation, Normalized solutions of a transmission problem of Kirchhoff type, The existence of normalized solutions for a fractional Kirchhoff-type equation with doubly critical exponents

Cites Work

• Unnamed Item
• Energy estimates and symmetry breaking in attractive Bose-Einstein condensates with ring-shaped potentials
• Ground state sign-changing solutions for Kirchhoff type problems in bounded domains
• Existence and concentration result for the Kirchhoff type equations with general nonlinearities
• 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 existence of normalized solutions for \(L^2\)-critical constrained problems related to Kirchhoff equations
• 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 Schrödinger equations and sharp interpolation estimates
• Problèmes isoperimetriques et espaces de Sobolev
• On Kirchhoff type equations with critical Sobolev exponent
• Existence of a positive solution for a Kirchhoff problem type with critical growth via truncation argument
• Existence and uniqueness of normalized solutions for the Kirchhoff equation
• Positive solutions to Kirchhoff type equations with nonlinearity having prescribed asymptotic behavior
• Existence of positive ground state solutions for the nonlinear Kirchhoff type equations in \(\mathbb{R}^3\)
• The critical problem of Kirchhoff type elliptic equations in dimension four
• Concentrating Bound States for Kirchhoff Type Problems in ℝ³ Involving Critical Sobolev Exponents
• The sharp existence of constrained minimizers for a class of nonlinear Kirchhoff equations
• Existence and multiplicity results for some superlinear elliptic problems on R^N
• Stability of attractive Bose-Einstein condensates