The multiplicity of radial \(k\)-convex solutions for an augmented Hessian equation

DOI10.1016/J.JMAA.2023.127408zbMath1519.35133OpenAlexW4376274576MaRDI QIDQ6110875

Lihong Zhang, Guotao Wang, Yu Zhang, Bashir Ahmad

Publication date: 6 July 2023

Published in: Journal of Mathematical Analysis and Applications (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/j.jmaa.2023.127408

zbMATH Keywords

sub-super-solution methodaugmented Hessian equationmultiplicity of radial \(k\)-convex solutions

Mathematics Subject Classification ID

Nonlinear elliptic equations (35J60) Existence problems for PDEs: global existence, local existence, non-existence (35A01) Monge-Ampère equations (35J96)

Related Items (1)

Existence results for the \(k\)-Hessian type system with the gradients via \(\mathbb{R}_+^n\)-monotone matrices

Cites Work

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• Bounded solutions of a \(k\)-Hessian equation in a ball
• Bernstein theorem and regularity for a class of Monge-Ampère equations
• Oblique boundary value problems for augmented Hessian equations. II
• The Dirichlet problem for nonlinear second order elliptic equations. III: Functions of the eigenvalues of the Hessian
• Boundary blow-up problems for Hessian equations
• Optimal boundary regularity for a singular Monge-Ampère equation
• Second-order estimates and regularity for fully nonlinear elliptic equations on Riemannian manifolds
• Liouville property and existence of entire solutions of Hessian equations
• Non-degeneracy and uniqueness of the radial solutions to a coupled \(k\)-Hessian system
• The radial solution for an eigenvalue problem of singular augmented Hessian equation
• On the Dirichlet problem for general augmented Hessian equations
• On the Dirichlet problem for a class of augmented Hessian equations
• Existence and nonexistence of subsolutions for augmented Hessian equations
• Optimal global and boundary asymptotic behavior of large solutions to the Monge-Ampère equation
• The existence and asymptotic behavior of boundary blow-up solutions to the \(k\)-Hessian equation
• Hessian equations on exterior domain
• Regularity of potential functions of the optimal transportation problem
• On the Dirichlet problem for Monge-Ampère type equations
• Some existence results for fully nonlinear elliptic equations of monge-ampère type

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